Introduction to Mathematical LogicRetaining all the key features of the previous editions, Introduction to Mathematical Logic, Fifth Edition explores the principal topics of mathematical logic. It covers propositional logic, first-order logic, first-order number theory, axiomatic set theory, and the theory of computability. The text also discusses the major results of Godel, Church |
Contents
Chapter 1 The Propositional Calculus | 1 |
Chapter 2 FirstOrder Logic and Model Theory | 41 |
Chapter 3 Formal Number Theory | 149 |
Chapter 4 Axionmatic Set Theory | 227 |
Chapter 5 Computability | 309 |
SecondOrder Logic | 375 |
First Steps in Modal Propositional Logic | 391 |
Answers to Selected Exercises | 403 |
| 433 | |
Notation | 447 |
| 453 | |
Back cover | 471 |
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Common terms and phrases
apply Assume axiom of choice axiom schema axiomatic cardinal numbers closed wf computation consistent contradicting Corollary ð Þ deduction theorem defined definition denote denumerable domain element equinumerous example Exercise expressible false finite number first-order theory formulas free variables function f function letters Gödel number Hence individual constants inductive hypothesis infinite isomorphic Kripke frame language Lemma logically equivalent logically valid mathematical natural numbers nonempty normal algorithm normal model obtained occurrences one–one ordinal partial recursive function positive integers predicate calculus predicate letter prenex normal form primitive recursive primitive recursive function proper axioms Proposition provable Prove quantifiers real numbers recursive or recursive recursively undecidable relation replace rule A4 satisfies sentence sequence set theory Show standard interpretation statement form statement letters subset symbols tape description tautology theory with equality transfinite induction true truth table truth values Turing machine well-ordering