Introduction to the Theory of Logic
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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FirstOrder Languages without Identity
FirstOrder Languages with Identity
A WellRounded Set of Sentences Is the Theory of its Canonical Structure
Henkin Constants and Henkin Axioms
Consistent NegationComplete Henkin Sets Are Well Rounded
Criteria for Size Claims
Big and Small
12 Zorns Lemma
Completeness for Uncountable Languages
Isomorphic Structures and Contextual Definitions
Representing Finite Structures
The Downward LowenheimSkolem Theorem
Symbols and Notation
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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Dr Read: Teaching
Preliminary Reading:. rr Stoll, Set Theory and Logic; G. Forbes, Modern Logic; J. Zalabardo, Introduction to the Theory of Logic ...
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