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A Mathematical Introduction to Logic
A Mathematical Introduction to Logic, Second Edition, offers increased flexibility with topic coverage, allowing for choice in how to utilize the textbook in a course. The author has made this edition more accessible to better meet the needs of today's undergraduate mathematics and philosophy students. It is intended for the reader who has not studied logic previously, but who has some experience in mathematical reasoning. Material is presented on computer science issues such as computational complexity and database queries, with additional coverage of introductory material such as sets.
USEFUL FACTS ABOUT SETS SENTENTIAL LOGIC Informal Remarks on Formal Languages The Language of Sentential Logic Induction and Recursion Truth Assignments Unique Readability Sentential Connectives Switching Circuits Compactness and Effectiveness FIRST-ORDER LOGIC Preliminary Remarks First-Order Languages Truth and Models Unique Readability A Deductive Calculus Soundness and Completeness Theorems Models of Theories Interpretations between Theories Nonstandard Analysis UNDECIDABILITY Number Theory Natural Numbers with Successor Other Reducts of Number Theory A Subtheory of Number Theory Arithmetization of Syntax Incompleteness and Undecidability Applications to Set Theory Representing Exponentiation Recursive Functions SECOND-ORDER LOGIC Second-Order Languages Skolem Functions Many-Sorted LogicGeneral Structures