ISBN: Ostalo
Godina izdanja: 1966
Jezik: Engleski
Oblast: Matematika
Autor: Strani

Roger C. Lyndon - Notes on Logic
D. Van Nostrand Company, Inc., 1966
97 str.
meki povez
stanje: vrlo dobro, potpis na predlistu.

Van Nostrand Mathematical Studies #6

These are notes from a course for advanced
undergraduate and beginning graduate students
in mathematics and related subjects which the
author taught at the University of Michigan in
the fall terms of 1962 and 1963. The attempt
has been made to present the notes as simply as
rigor permits, giving them something of the
spirit of elementary abstract algebra. The sub-
ject matter, which can be seen from the Table of
Contents, is all well known, and only occasion-
ally have references been given.
The author wishes to state expressly his
debt over many year to Alfred Tarski, with the
ho`pe that some of his ideas will be visible in
these notes. The author is especially grateful
to J ames Bennett for reading the manuscript.
R. C. L.

TABLE OF CONTENTS
Preface . . . . . . . . . . . . . . . . . . . .
Introduction. . . . . . . .`. . . . . .
Program . . . . . . . . . . . . . . . .
Grammar. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Terms . . . . . . . . . . . .
Formulas and Sentences ......................
Interpretations and Structures . . . . . . . . . . . . . . . . . . .
Dependence and Substitution ...................
Semantic Implication . . . . . . . . . . . . . . . . . . . . . . . . .
Sentential Logic ...........................
The Algebra of Propositions . . . . . . . . . . . . . . . . . . . .
Disjunctive Form . . . . . . . . . . . . . . . . . . . . . . .
Boolean Algebra. . . . . . . . . . . . . . . . . . . . . . . . . . . .
Variants of Sentential Logic. . . . . . . . . . . . . . . . . . . .
Decidability and Axiomatizability . . . . . . . . . . . . . . . .
Decidable Theories .........................
Axiomatization of Predicate Logic . . . . . . . . . . . . . . . .
Validity of the Axiomatization. . . . . . . . . . . . . . . . . . .
The Deduction Theorem. . . . . . . . . . . . . . . . . . . . . . .
The Consistency Theorem . . . . . . . . . . . . . . . . . . . . .
The Adequacy Theorem and Compactness Theorem . . . . .
Predicate Logic with Identity . . . . . . . . . . . . . . . . . . .
The Lowenheim Skolem Theorem . . . . . . . . . . . . . . . . .
Categoricity .. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
VI Table of Contents
Gentzen`s Natural Inference . . . . . . . . . . . . . . . . . . . . .
Second Formulation. . . . . . . . . . . . . . . . . . . . . . . . .
The Adequacy Theorem . . . . . . . . . . . . . . . . . . . . . . . .
The Herbrand Gentzen Theorem. . . . . . . . . . . . . . . . . . .
Craig`s Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Diagonal Arguments and the Paradoxes .............
Godel Numbers .. · · · · · · · · · · · · · · · · · · · · · · · · · · ·
Expressibility and Tarski`s Theorem . . . . . . . . . . . . . . .
Godel`s Incompleteness Theorem. . . . . . . . . . . .. . . . . . .
Decidability and Church`s Theorem . . . . . . . . . . . . . . . .
The Unprovability of Consistency . . . . . . . . . . . . . . . . .
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Index of Names
Index of Terms


Nonfiction, Mathematics