Introduction to Mathematical Logic, Fourth EditionThe Fourth Edition of this long-established text retains all the key features of the previous editions, covering the basic topics of a solid first course in mathematical logic. This edition includes an extensive appendix on second-order logic, a section on set theory with urlements, and a section on the logic that results when we allow models with empty domains. The text contains numerous exercises and an appendix furnishes answers to many of them. Introduction to Mathematical Logic includes: The study of mathematical logic, axiomatic set theory, and computability theory provides an understanding of the fundamental assumptions and proof techniques that form basis of mathematics. Logic and computability theory have also become indispensable tools in theoretical computer science, including artificial intelligence. Introduction to Mathematical Logic covers these topics in a clear, reader-friendly style that will be valued by anyone working in computer science as well as lecturers and researchers in mathematics, philosophy, and related fields. |
Contents
Quantification theory | 52 |
Formal number theory | 154 |
Axiomatic set theory | 225 |
Computability | 305 |
Appendix Secondorder logic | 368 |
Answers to selected exercises | 383 |
Bibliography | 412 |
Notation | 424 |
Common terms and phrases
a₁ applied Assume axiom of choice axiom schema axiomatic b₁ cardinal numbers closed wf computation consistent contradicting Corollary deduction theorem defined definition denote denumerable element equinumerous example Exercise expression finite number first-order theory following wfs formulas free variables function f function letters Gödel number Hence individual constants infinite k₁ language Lemma logically valid M₁ mathematical natural numbers non-empty normal algorithm normal model obtain occurrences one-one ordinal partial recursive function positive integers predicate calculus predicate letter prenex normal form primitive recursive Proposition provable Prove quantifiers real numbers recursive or recursive recursively undecidable relation replace rule A4 satisfies second-order logic sentence sequence set theory Show statement form statement letters subset symbols tape description tautology theory with equality transfinite induction true truth table truth values Turing machine well-ordering x₁