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1.
Zbl 0989.03001
Rautenberg, Wolfgang
Einführung in die mathematische Logik. Ein Lehrbuch. (Introduction to mathematical logic. A textbook). 2., verbesserte und erweiterte Aufl.
(German)
[B] Wiesbaden: Vieweg. 256 p. EUR 26.90; sFr. 47.10 (2001). [ISBN 3-528-16754-8/pbk]
This is the second improved and extended edition (the first one was published in 1996 under the same title; see
Zbl 0866.03001
) of the textbook on mathematical logic for university students. The general concept of the book was not changed, the chapters are the same: 1) Propositional logic; 2) Predicate logic; 3) Gödel's completeness; 4) Elements of logic programming; 5) Elements of model theory; 6) Incompleteness and undecidability; 7) Self-reference theory. But the text was thoroughly revised in details. Chapters 6 and 7 were essentially changed, extended, and newly organized. The book is sufficiently up-to-date, the main instrument of formal proofs is Gentzen's natural inference, which is nearest to the usual run of mathematical reasoning. Gödel's modal logic G (chapter 7), which formalizes the part of the proof theory which concerns self-referential formulas (they state their own unprovability) is considered for the first time in the educational literature.
[
A.Nabebin
(Moskva)
]
MSC 2000:
*
03-01
Textbooks (mathematical logic)
68N17
Logic programming
Keywords:
mathematical logic; formal inference; logic programming; model theory; algorithm theory; proof theory; modal logic; self-referential formual
Citations:
Zbl 0866.03001
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2.
Zbl 0866.03001
Rautenberg, Wolfgang
Einführung in die mathematische Logik. Ein Lehrbuch mit Berücksichtigung der Logikprogrammierung. (Introduction to mathematical logic. A textbook considering logic programming).
(German)
[B] Lehrbuch Mathematik. Wiesbaden: Vieweg. xii, 250 p. DM 39.50 (1996). [ISBN 3-528-06754-3/pbk]
The textbook in mathematical logic is written for university students. It deals with the basic notions of mathematical logic and formal inference. Resolution and Prolog programming are also introduced.\par The book's goal is to provide three main theorems of mathematical logic: 1) Gödel's theorem about the completeness of predicate calculus with respect to the set of valid first-order predicate formulas (true in every possible interpretation); 2) Church's theorem about algorithmic undecidability of predicate calculus; 3) Gödel's theorem about the incompleteness of axiomatic arithmetic (with respect to the semantically true formulas of arithmetic). A result of Tarski is expounded on the way: the set of all true formulas of arithmetic is not arithmetical. The solution of Hilbert's 10th problem is also outlined.\par Recursive function theory is presented in the amount necessary for the proof of the main theorems. Formalisms are described in the form of Gentzen natural deduction, which is nearest to the usual run of mathematical reasoning. The axiomatic approach of Hilbert is expounded as another form of representation of valid first-order predicate formulas.\par The author has chosen those notions and theorems in the area of mathematical logic that allow him to come to the three main theorems most quickly and economical, and to make the proofs of the intermediate facts transparent and elegant.\par Very nice is the chapter about Gödel's modal logic G, which formalizes the part of proof theory which concerns the self-referential formulas (they state their own unprovability). Algorithmic decidability of G is proved with the help of Kripke models (result of R. Solovay). The material is presented with clear semantics and syntax.\par The order of the chapters is as follows: 1) Propositional logic; 2) Predicate logic; 3) Gödel's completeness; 4) Elements of logic programming; 5) Elements of model theory; 6) Incompleteness and undecidability; 7) Self-referential theory.\par The book can be useful to the student and lecturer who prepares a mathematical logic course at the (technical) university.\par What a pity that the book is not written in a universal scientific language which mankind have not yet created.
[
A.Nabebin
(Moskva)
]
MSC 2000:
*
03-01
Textbooks (mathematical logic)
68N17
Logic programming
Keywords:
logic programming; model theory; algorithm theory; proof theory; modal logic; self-referential formula; mathematical logic
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3.
Zbl 0925.03109
Pearce, David
;
Rautenberg, Wolfgang
Propositional logic based on the dynamics of disbelief.
(English)
[CA] Fuhrmann, André (ed.) et al., The logic of theory change. Workshop, Konstanz, Germany, October 13-15, 1989. Proceedings. Berlin etc.: Springer-Verlag. Lect. Notes Comput. Sci. 465, 243-258 (1991). [ISBN 3-540-53567-5; ISSN 0302-9743; ISSN 0302-9743]
Not reviewed
MSC 2000:
*
03B45
Modal logic, etc.
03B60
Other nonclassical logic
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4.
Zbl 0824.00001
Rautenberg, Wolfgang
Elementare Grundlagen der Analysis. (Elementary foundations of analysis).
(German)
[B] Mannheim: BI Wissenschaftsverlag. xii, 152 p. DM 19.80; öS 155.00; sFr. 19.80 (1993). [ISBN 3-411-16611-8/pbk]
Das vorliegende Büchlein gibt einen Aufbau des Zahlensystems, also eine axiomatische Grundlegung der Analysis. Dabei werden die natürlichen Zahlen zunächst als gegeben hingenommen und diejenigen ihrer Rechenregeln bereitgestellt, die bei Erweiterung zu anderen Bereichen nichtnegativer Zahlen, z.B. endliche Dezimalzahlen, ihre Gültigkeit behalten. Sodann präsentiert Verf. schon an sehr früher Stelle die von ihm entwickelte explizite Konstruktion der reellen Zahlen, ausgehend von dezimalen Kommazahlen. \par Die einzelnen Abschnitte sind wie folgt überschrieben: Zur Geschichte des Zahlbegriffs, natürliche Zahlen und Rechenregeln, reelle Zahlen und ihre Anordnung, Arithmetik der abbrechenden Dezimalzahlen, Arithmetik der reellen Zahlen, Division und rationale Zahlen, beginnende Analysis, elementare Rechenalgorithmen, negative und komplexe Zahlen, Maßzahlen und Operatoren, Anhang: die natürlichen Zahlen. Die Abschnitte schließen mit Übungsaufgaben, die am Ende des Büchleins vollständig gelöst sind; Übungen und Lösungen machen ein Achtel des Buchumfangs aus. \par Die Lektüre erfordert keine speziellen mathematischen Vorkenntnisse, wohl aber gewisse Fertigkeiten im logischen Schließen. Das Buch kann Mathematik- und Informatikstudenten als Ergänzungstext zur Analysisvorlesung, vor allem aber Lehramtskandidaten empfohlen werden, da wichtige Gegenstände behandelt werden, für die in universitären Anfängerkursen meist nicht genügend Zeit bleibt.
[
P.Bundschuh
(Köln)
]
MSC 2000:
*
00A05
General mathematics
00-01
Textbooks (general mathematics)
Keywords:
arithmetic; analysis; number system; real numbers; decimal numbers
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5.
Zbl 0771.03003
Rautenberg, Wolfgang
On reduced matrices.
(English)
[J]
Stud. Log.
52, No.1, 63-72 (1993). [ISSN 0039-3215]
It is shown that the class of reduced matrices of a logic $\vdash$ is a first order $\forall\exists$-class provided the variety associated with $\vdash$ has the finite replacement property in the sense of the author's joint paper with {\it B. Herrmann} [``Finite replacement and finite Hilbert-style axiomatizability'', Z. Math. Logik Grundlagen Math. (to appear)]. This applies in particular to all 2-valued logics. For 3-valued logics the class of reduced matrices need not be first order.
MSC 2000:
*
03B22
Abstract deductive systems
03B20
Subsystems of classical logic
08B05
Equational logic in varieties of algebras
03B50
Many-valued logic
Keywords:
reduced matrices of a logic; variety; finite replacement property; 2- valued logics; 3-valued logics
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6.
Zbl 0794.03047
Rautenberg, Wolfgang
Der Gödelsche Vollständigkeitssatz. (Gödel's completeness theorem).
(German)
[J]
Math. Semesterber.
39, No.1, 13-28 (1992). [ISSN 0720-728X]
Der hier dargebotene Beweis des Gödelschen Vollständigkeitssatzes setzt für sein Verständnis nur Anfangskenntnisse der Logik voraus (was ist ein Term, eine Formel, ein Modell). Es werden je ein Gentzen- und ein Hilbert-Kalkül als vollständig nachgewiesen. Die Beweise sich nicht neu im Prinzip, wohl aber in einigen nicht unwesentlichen Details und daher relativ kurz. Es werden auch die wichtigsten Konsequenzen des Satzes erörtert.
MSC 2000:
*
03C07
Basic properties of first-order languages and structures
03-01
Textbooks (mathematical logic)
Keywords:
Gödel's completeness theorem; Gentzen calculus; Hilbert calculus
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7.
Zbl 0747.03001
Rautenberg, Wolfgang
Unvollständigkeit, Unentscheidbarkeit, Nichtdefinierbarkeit. (Incompleteness, undecidability, undefinability).
(German)
[R] Mitt. Math. Semin. Gießen 202, 36 p. (1991). [ISSN 0373-8221]
This neat and commendable exposition of the incompleteness theorems resulted from lectures given to mathematics students on the occasion of the sixtieth birthday of Gödel's famous 1931 paper. In six paragraphs the author treats recursive and primitive-recursive functions, representability of recursive functions in R. M. Robinson's system Q, Gödelization of syntax, the fixpoint-lemma and the theorems of Gödel, Tarski and Church, and, finally, the second incompleteness theorem, with Löb's theorem and later results due to R. Solovay, D. de Jongh and G. Sambin.
[
W.Veldman
(Nijmegen)
]
MSC 2000:
*
03-01
Textbooks (mathematical logic)
03D35
Undecidability
03F40
Goedel numberings in proof theory
Keywords:
incompleteness theorems; recursive functions; Gödelization; fixpoint- lemma; Löb's theorem
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8.
Zbl 0741.03003
Rautenberg, Wolfgang
Common logic of 2-valued semigroup connectives.
(English)
[J]
Z. Math. Logik Grundlagen Math.
37, No.2, 187-192 (1991). [ISSN 0044-3050]
Suppose $f$ and $g$ are sets of binary propositional connectives with $f\subseteq g$. $\vdash\sp f$ and $\vdash\sp g$ denote the common sequential rules for $f$ and $g$, respectively. $\vdash\sp f$ is a strengthening of $\vdash\sp g$, if $\vdash\sp g$ is a conservative extension of $\vdash\sp f$. Let $*$ denote the set of connectives $\{\land,\lor,\leftrightarrow,+\}$, where $+$ is either-or. The author shows that $\vdash\sp*$ has exactly 25 proper strengthenings, each of which is determined by finitely many finite matrices.
[
C.F.Kielkopf
(Columbus)
]
MSC 2000:
*
03B22
Abstract deductive systems
Keywords:
binary propositional connectives; sequential rules; strengthening; conservative extension
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9.
Zbl 0715.03003
Rautenberg, Wolfgang
Common logic of binary connectives has finite maximality degree.
(English)
[J] Bull. Sect. Log., Pol. Acad. Sci. 19, No.2, 36-38 (1990).
The title says it all. The connectives considered in this note are interpreted as binary Boolean functions f: 2${}\sp 2\to 2$ that depend on both arguments. The main result reads that the common logic of binary connectives has finitely many structural strengthenings and that all the strengthenings are defined by finitely many finite matrices.
[
Z.Stachniak
]
MSC 2000:
*
03B20
Subsystems of classical logic
03B22
Abstract deductive systems
Keywords:
degree of maximality; binary Boolean functions; common logic of binary connectives; structural strengthenings; finite matrices
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10.
Zbl 0707.03006
Rautenberg, Wolfgang
A calculus for the common rules of $\wedge$ and $\vee$.
(English)
[J]
Stud. Log.
48, No.4, 531-537 (1989). [ISSN 0039-3215]
Let $\vdash\sp*$ denote the common sequential rules for $\wedge$ and $\vee$. Let $\vdash\sp{\wedge}$ denote the sequential rules for $\wedge$, and $\vdash\sp{\vee}$ denote those for $\vee$. The author's main questions are: (a) Is $\vdash\sp*$ finitely based?, and: (b) Are $\vdash\sp{\wedge}$ and $\vdash\sp{\vee}$ the only proper non-trivial strengthenings of $\vdash\sp*?$ As his work shows: ``Both questions have a positive answer, but the proofs are not as easy as one might expect.'' But his work has far greater theoretical and technical interest than these two questions about $\wedge$ and $\vee$ might indicate. He indicates how such question might be of interest to computer science. His work brings out that there are challenging problems in the area of asking analogous questions for other dual operators.
[
C.F.Kielkopf
]
MSC 2000:
*
03B22
Abstract deductive systems
Keywords:
dual connectives; finite axiomatizability; common sequential rules for $\wedge $ and $\vee $
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11.
Zbl 0688.03017
Rautenberg, Wolfgang
Axiomatization of semigroup consequences.
(English)
[J]
Arch. Math. Logic
29, No.2, 111-123 (1989). [ISSN 0933-5846]
A semigroup connective is a binary connective which is associative and properly binary. Of the 16 binary connectives only 10 are properly binary and of these only: $\wedge$, $\vee$, $\leftrightarrow$, $+$, are associative. With logics represented as rules placing conditions on consequence relations, a general problem is to specify the common rules for two or more semigroup connectives. A more specific problem is to specify conditions for a finitely based set of common rules. The author uses matrix semantics to show: The consequence relation determined by a variety V of algebraic semigroup matrices is finitely based iff V is finitely based. He then proves that the common rules for the connectives: $\wedge$, $\vee$, $\leftrightarrow$, $+$ are finitely based. \par The first line of Section 1 on p. 115 should read: We are now going to construct an effective base.
[
C.F.Kielkopf
]
MSC 2000:
*
03B99
General logic
Keywords:
semigroup connective; consequence relations; matrix semantics
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12.
Zbl 0673.03022
Rautenberg, Wolfgang
The common rules of binary connectives are finitely based.
(English)
[J] Bull. Sect. Logic, Pol. Acad. Sci. 18, No.2, 87-89 (1989).
The author presents some statements related to the notions of finitely based and independent propositional logics, generalizing some of his earlier results [Stud. Logica 40, 315-353 (1981;
Zbl 0493.03006
); Foundations of Logic and Linguistics, Sel. Pap. 7th Int. Congr. Logic, Methodol. Philos. Sci., Salzburg/Austria 1983, 3-22 (1985;
Zbl 0623.03034
)]. The paper contains a sequence of interesting remarks and examples concerning the applications of these statements in the fields of logic, algebra, linguistics and systems of information processing.
[
B.R.Boricic
]
MSC 2000:
*
03B99
General logic
03G99
Algebraic logic
Keywords:
finitely based logics; independent propositional logics
Citations:
Zbl 0493.03006
;
Zbl 0623.03034
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13.
Zbl 0676.03021
Rautenberg, Wolfgang
A note on completeness and maximality in propositional logic.
(English)
[J]
Rep. Math. Logic
21, 3-8 (1987). [ISSN 0137-2904]
A structural consequence relation without nontrivial structural extensions is treated. For that relation, a simple method of proving completeness and maximality is given through examples.
[
T.Hosoi
]
MSC 2000:
*
03B99
General logic
Keywords:
structural consequence relation; completeness; maximality
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14.
Zbl 0637.03047
Rautenberg, Wolfgang
Über den Cantor-Bernsteinschen Äquivalenzsatz. (On the Cantor- Bernstein theorem).
(German)
[J]
Math. Semesterber.
34, 71-88 (1987). [ISSN 0720-728X]
Not reviewed
MSC 2000:
*
03E20
Other classical set theory (logic)
03E30
Axiomatics of classical set theory and its fragments
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15.
Zbl 0635.03020
Rautenberg, Wolfgang
Applications of weak Kripke semantics to intermediate consequences.
(English)
[J]
Stud. Log.
45, 119-134 (1986). [ISSN 0039-3215]
The author first proves the completeness of weak Kripke semantics for intermediate consequences, then he applies the completeness theorem to the study of minute structure of so-called counterslices. Implicationless fragments are also treated.
[
T.Hosoi
]
MSC 2000:
*
03B55
Intermediate logics
Keywords:
intermediate logic; completeness of weak Kripke semantics for intermediate consequences; counterslices; Implicationless fragments
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16.
Zbl 0632.26002
Rautenberg, Wolfgang
Zur Approximation von e durch $(1+1/n)\sp n$. (On the approximation of e by $(1+1/n)\sp n)$.
(German)
[J]
Math. Semesterber.
33, 227-236 (1986). [ISSN 0720-728X]
Not reviewed
MSC 2000:
*
26A06
One-variable calculus
65B99
Acceleration of convergence
Keywords:
approximation of e; error bounds
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17.
Zbl 0623.03034
Rautenberg, Wolfgang
Consequence relations of 2-element algebras.
(English)
[CA] Foundations of logic and linguistics, Sel. Pap. 7th Int. Congr. Logic, Methodol. Philos. Sci., Salzburg/Austria 1983, 3-22 (1985).
[For the entire collection see
Zbl 0598.00008
.] \par We show that the consequence determined by a 2-element algebra has at most 7 proper non-trivial extensions and that it is finitely axiomatizable with sequential rules. This implies among other things the finite axiomatizability of each 2-valued consequence in a finite language.
MSC 2000:
*
03B99
General logic
Keywords:
consequence relations; 2-element algebra; finite axiomatizability
Citations:
Zbl 0598.00008
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18.
Zbl 0547.03015
Rautenberg, Wolfgang
Modal tableau calculi and interpolation.
(English)
[J] J. Philos. Logic 12, 403-423 (1983).
The paper shows that all the propositional modal calculi over the language whose connectives are $\neg$, $\wedge$, $\square$ and $\bigcirc$ (falsum) and which possess a complete tableau system have the interpolation property, provided that the tableau rules satisfy certain conditions. These conditions include a wide class of normal modal calculi. The author also presents tableau systems for several modal calculi (including B, K4, G, Gr and extensions) and proves by constructive methods the completeness of those tableau systems with respect to appropriate Kripke semantics. It is shown, specifically, that the finite model property holds for those systems, which also satisfy the remaining conditions for the interpolation property. The problem of the existence of the interpolation property is discussed for various other examples, in particular for some classes of extensions of K4, G and Gr.
[
W.Carnielli
]
MSC 2000:
*
03B45
Modal logic, etc.
03C40
Interpolation, etc. (model theory)
Keywords:
propositional modal calculi; tableau system; interpolation property; normal modal calculi; Kripke semantics; finite model property
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19.
Zbl 0535.03003
Rautenberg, Wolfgang
Results and problems concerning fragments of classical propositional logic.
(English)
[J] Bull. Sect. Logic, Pol. Acad. Sci. 11, 69-71 (1982).
The author has posed the following problems: (1) Give a Post- classification-free proof of the statement that each two-valued consequence is strongly finitely axiomatizable. (2) What is the free spectrum of expansions of the two-element algebra with implication? (3) Is the (strong) identification problem $\vdash =K\vdash$ solvable for $\vdash \supseteq BCK\vdash$, where BC$K\vdash$ denote the BCK-calculus [see, e.g., {\it K. Iséki} and {\it S. Tanaka}, Math. Japonica 23, 1-26 (1978;
Zbl 0385.03051
)] and $K\vdash$ the classical calculus in $\to ?$ The paper contains useful comments to the given problems and two statements which could be essential steps in solving the first problem. For a better understanding of the paper it is necessary to be familiar with some earlier works of the same author [e.g., Stud. Logica 40, 315- 353 (1981;
Zbl 0493.03006
)].
[
B.R.Boricic
]
MSC 2000:
*
03B20
Subsystems of classical logic
Keywords:
finite axiomatizability; consequence operation; free spectrum of expansions of the two-element algebra with implication; identification problem; BCK-calculus
Citations:
Zbl 0385.03051
;
Zbl 0493.03006
Cited in Zbl. reviews...
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20.
Zbl 0493.03006
Rautenberg, Wolfgang
2-element matrices.
(English)
[J]
Stud. Log.
40, 315-353 (1981). [ISSN 0039-3215]
See printed version
MSC 2000:
*
03B99
General logic
03G99
Algebraic logic
03C05
Universal algebra (model theory)
Keywords:
strong finite axiomatizability of all 2-valued matrices; Post's classification; algebraic properties of 2-element algebras; equational completeness; Stone-property; minimal quasivariety; matrix free characterization of 2-valued consequences; lattice of structural consequences; axiomatization problems for finite algebras and matrices; propositional consequence with equality; explicit axiomatizations of 2- valued consequences with equality
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21.
Zbl 0453.03017
Rautenberg, Wolfgang
Splitting lattices of logics.
(English)
[J]
Arch. Math. Logik Grundlagenforsch.
20, 155-159 (1980). [ISSN 0003-9268]
See printed version
MSC 2000:
*
03B45
Modal logic, etc.
Keywords:
splitting theorem; normal modal logics
Citations:
Zbl 0404.03055
;
Zbl 0265.08006
;
Zbl 0424.03007
Cited in Zbl. reviews...
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22.
Zbl 0425.00001
Rautenberg, Wolfgang
Reelle Zahlen in elementarer Darstellung.
(German)
[B] Klett Studienbücher Mathematik. Stuttgart: Ernst Klett Verlag. 181 S. DM 24.00 (1979).
See printed version
MSC 2000:
*
00-01
Textbooks (general mathematics)
12D15
Formally real fields
Keywords:
construction of R
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23.
Zbl 0424.03007
Rautenberg, Wolfgang
Klassische und nichtklassische Aussagenlogik.
(German)
[B] Logik und Grundlagen der Mathematik, Bank 22. Braunschweig/Wiesbaden: Friedr. Vieweg \& Sohn. XI, 361 S, zahlr. Fig. DM 39.80 (1979).
See printed version
MSC 2000:
*
03B05
Classical propositional logic
03B45
Modal logic, etc.
03B50
Many-valued logic
03G10
Lattices and related structures (algebraic logic)
03G20
Post and Lukasiewicz algebras (algebraic logic)
03-01
Textbooks (mathematical logic)
03-02
Research monographs (mathematical logic)
Keywords:
propositional calculus; algebraic semantics; ultrafilter theory; classical sentential calculus; axiomatic and deductive systems without quantifiers; intuitionistic logic; constructive logical systems
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24.
Zbl 0411.03015
Rautenberg, Wolfgang
More about the lattice of tense logics.
(English)
[J] Bull. Sect. Logic, Pol. Acad. Sci. 8, 21-26 (1979).
See printed version
MSC 2000:
*
03B45
Modal logic, etc.
Keywords:
lattice of tense logics
Citations:
Zbl 0411.03014
Cited in Zbl. reviews...
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25.
Zbl 0411.03014
Rautenberg, Wolfgang
The lattice of ramified modal and tense logic (preliminary report).
(English)
[J] Bull. Sect. Logic, Pol. Acad. Sci. 7, 31-33 (1978).
See printed version
MSC 2000:
*
03B45
Modal logic, etc.
Keywords:
lattice of ramified modal and tense logic
Citations:
Zbl 0411.03015
Cited in Zbl. reviews...
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26.
Zbl 0404.03055
Rautenberg, Wolfgang
The lattice of normal modal logics (Preliminary report).
(English)
[J] Bull. Sect. Logic, Pol. Acad. Sci. 6, 193-201 (1977).
See printed version
MSC 2000:
*
03G10
Lattices and related structures (algebraic logic)
03B45
Modal logic, etc.
08B15
Lattices of varieties of algebras
06D20
Heyting algebras
Keywords:
SPLITTINGS OF LATTICES OF NORMAL MODEL LOGICS; FINITE SUBDIRECT IRREDUCIBLE MODAL ALGEBRAS; VARIETIES; HEYTING ALGEBRA
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27.
Zbl 0324.02041
Korec, Ivan
;
Rautenberg, Wolfgang
Model-interpretability into trees and applications.
(English)
[J]
Arch. Math. Logik Grundlagenforsch.
17, 97-104 (1976). [ISSN 0003-9268]
See printed version
MSC 2000:
*
03C60
Model-theoretic algebra
03B25
Decidability of theories and sets of sentences
05C99
Graph theory
05C05
Trees
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28.
Zbl 0314.02001
Rautenberg, Wolfgang
Eine Synthese der axiomatischen und der kardinalen Definition der natürlichen Zahlen.
(German)
[J] Math.-Phys. Semesterber., N. F. 22, 225-239 (1975).
See printed version
MSC 2000:
*
03-01
Textbooks (mathematical logic)
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29.
Zbl 0319.02035
Hauschild, Kurt
;
Rautenberg, Wolfgang
Entscheidungsprobleme der Theorie zweier Äquivalenzrelationen mit beschränkter Zahl von Elementen in den Klassen.
(German)
[J]
Fundam. Math.
81(1973), 35-41 (1974). [ISSN 0016-2736]
See printed version
MSC 2000:
*
03B25
Decidability of theories and sets of sentences
03E20
Other classical set theory (logic)
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30.
Zbl 0305.02002
Franzke, Norbert
;
Rautenberg, Wolfgang
Zur Geschichte der Logik in Polen.
(German)
[CA] Quantoren-Modalitäten-Paradoxien, Beitr. Logik, 33-94 (1972).
See printed version
MSC 2000:
*
03-03
Historical (mathematical logic)
01A60
Mathematics in the 20th century
01A55
Mathematics in the 19th century
Citations:
Zbl 0237.00011
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31.
Zbl 0284.02023
Hauschild, Kurt
;
Herre, Heinrich
;
Rautenberg, Wolfgang
Interpretierbarkeit und Entscheidbarkeit in der Graphentheorie. II.
(German)
[J]
Z. Math. Logik Grundlagen Math.
18, 457-480 (1972). [ISSN 0044-3050]
See printed version
MSC 2000:
*
03B25
Decidability of theories and sets of sentences
03B99
General logic
05C99
Graph theory
Cited in Zbl. reviews...
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32.
Zbl 0264.02046
Hauschild, Kurt
;
Herre, Heinrich
;
Rautenberg, Wolfgang
Entscheidbarkeit der monadischen Theorie 2. Stufe der n-separierten Graphen.
(German)
[J] Wiss . Z. Humboldt-Univ. Berlin, Math.-naturw. R. 21, 507-511 (1972).
See printed version
MSC 2000:
*
03B25
Decidability of theories and sets of sentences
05C99
Graph theory
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33.
Zbl 0252.02050
Hauschild, Kurt
;
Herre, Heinrich
;
Rautenberg, Wolfgang
Entscheidbarkeit der elementaren Theorie der endlichen Bäume und verwandter Klassen endlicher Strukturen.
(German)
[J] Wiss. Z. Humboldt-Univ. Berlin, Math.-naturw. R. 21, 497-502 (1972).
See printed version
MSC 2000:
*
03B25
Decidability of theories and sets of sentences
05C05
Trees
03C68
Other classical first-order model theory
05C20
Directed graphs (digraphs)
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34.
Zbl 0231.02058
Rautenberg, Wolfgang
;
Hauschild, Kurt
Interpretierbarkeit und Entscheidbarkeit in der Graphentheorie. I. (Interpretability and decidability in graph theory. I).
(German)
[J]
Z. Math. Logik Grundlagen Math.
17, 47-55 (1971). [ISSN 0044-3050]
See printed version
MSC 2000:
*
03D35
Undecidability
05C99
Graph theory
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35.
Zbl 0215.04801
Hauschild, Kurt
;
Rautenberg, Wolfgang
Interpretierbarkeit in der Gruppentheorie
(German)
[J]
Algebra Univers.
1, 136-151 (1971). [ISSN 0002-5240]
See printed version
MSC 2000:
*
03D35
Undecidability
03B25
Decidability of theories and sets of sentences
05C25
Graphs and groups
20K15
Torsion free abelian groups, finite rank
20E05
Free nonabelian groups
20Mxx
Semigroups
Cited in Zbl. reviews...
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36.
Zbl 0275.02043
Hauschild, Kurt
;
Rautenberg, Wolfgang
Universelle Interpretierbarkeit in Verbänden.
(English)
[J] Wiss. Z. Humboldt-Univ. Berlin, Math.-naturw. R. 19, 575-577 (1970).
See printed version
MSC 2000:
*
03B25
Decidability of theories and sets of sentences
03C60
Model-theoretic algebra
03C68
Other classical first-order model theory
06D05
Structure and representation theory of distributive lattices
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37.
Zbl 0275.02049
Herre, Heinrich
;
Rautenberg, Wolfgang
Das Basistheorem und einige Anwendungen in der Modelltheorie.
(German)
[J] Wiss. Z. Humboldt-Univ. Berlin, Math.-naturw. R. 19, 579-583 (1970).
See printed version
MSC 2000:
*
03C68
Other classical first-order model theory
Cited in Zbl. reviews...
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