Introduction to the Theory of Logic

Westview Press, 2000 - Philosophy - 330 pages
This book provides a rigorous introduction to the basic concepts and results of contemporary logic. It also presents, in two unhurried chapters, the mathematical tools (mainly from set theory) that are needed to master the technical aspects of the subject. Methods of definition and proof are also discussed at length, with special emphasis on inductive definitions and proofs and recursive definitions. The book is ideally suited for readers who want to undertake a serious study of logic but lack the mathematical background that other texts at this level presuppose. It can be used as a textbook in graduate and advanced undergraduate courses in logic. Hundreds of exercises are provided. Topics covered include basic set theory, propositional and first-order syntax and semantics, a sequent calculus-style deductive system, the soundness and completeness theorems, cardinality, the expressive limitations of first-order logic, with especial attention to the Loewenheim-Skolem theorems and non-standard models of arithmetic, decidability, complete theories, categoricity and quantifier elimination.

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The most comprehensible introduction to logic I've found. Read full review

Contents

 Chapter 36 Chapter 76 Chapter 117 Chapter 149 FirstOrder Languages without Identity 162 FirstOrder Languages with Identity 166 A WellRounded Set of Sentences Is the Theory of its Canonical Structure 170 Negation Completeness 174
 Exponentiation 201 Cardinality 204 Contextual Definition 206 Continuities 209 Denumerable Sets 215 Diagonals 218 ZF 224 11 Choice 228

 Henkin Constants and Henkin Axioms 178 Consistent NegationComplete Henkin Sets Are Well Rounded 183 Compactness 187 Chapter 189 Criteria for Size Claims 190 Counting 191 Functional Criteria 195 Big and Small 196 Addition 197 Multiplication 199
 12 Zorns Lemma 236 Completeness for Uncountable Languages 245 Chapter 250 Isomorphic Structures 252 Isomorphic Structures and Contextual Definitions 259 Representing Finite Structures 261 The Downward LowenheimSkolem Theorem 263 Chapter 292 Symbols and Notation 321 Copyright

Popular passages

Page 73 - ... f ...f •••t •••t ...f ...f ...t ...f ...f •••t •••t •••t •••t •••t •••t •••t •••t ...t •••t •••: ...t...
Page 238 - B be any two sets. The set of all ordered pairs such that the first member of the ordered pair is an element of A and the second member is an element of B is called the cartesian product of A and B and is written as AX B.
Page 8 - The intersection of sets A and B, written A n B, is the set of all elements common to sets A and B.
Page 117 - An argument will be said to be valid if and only if the conjunction of the premises implies the conclusion, ie, if the premises are all true, the conclusion must also be true. It...
Page xii - I have tried to present the material in such a way as to be intelligible and even helpful to graduate students and, perhaps, undergraduates.
Page 175 - Prove that there exists a one-to-one correspondence between the set of positive integers and the set of all positive rational numbers.
Page 8 - The union of sets A and B, written A u B, is the set whose elements are all the elements of A and all the elements of B.
Page 187 - ... then it is not the case that for every set F of sentences of intensional logic, (3) if every finite subset of F is satisfiable, then F is satisfiable. This is obvious in view of the reduction, at which we hinted earlier, of ordinary second-order logic to intensional logic, together with the wellknown failure of the compactness theorem for second-order logic. On the other hand, let us call \$ a predicative sentence if...

References from web pages

Introduction to the Theory of Logic by José L. Zalabardo at ...
Jose L. Zalabardo is a lecturer in the philosophy department at the University of Birmingham in England
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