Book:Ian Chiswell/Mathematical Logic

Volume 3 in the Oxford Texts in Logic series.

Subject Matter
Mathematical Logic

Contents

 * 1 Prelude
 * 1.1 What is mathematics?
 * 1.2 Pronunciation guide
 * 2 Informal natural deduction
 * 2.1 Proofs and sequents
 * 2.2 Arguments introducing 'and'
 * 2.3 Argumants eliminating 'and'
 * 2.4 Arguments using 'if'
 * 2.5 Arguments using 'if and only if'
 * 2.6 Arguments using 'not'
 * 2.7 Arguments using 'or'
 * 3 Propositional logic
 * 3.1 $\mathrm{LP}$, the language of propositions
 * 3.2 Parsing trees
 * 3.3 Propositional formulas
 * 3.4 Propositional natural deduction
 * 3.5 Truth tables
 * 3.6 Logical equivalence
 * 3.7 Substitution
 * 3.8 Disjunctive and conjunctive normal forms
 * 3.9 Soundness for propositional logic
 * 3.10 Completeness for propositional logic
 * 4 First interlude: Wason's selection task
 * 5 Quantifier-free logic
 * 5.1 Terms
 * 5.2 Relations and functions
 * 5.3 The language of first-order logic
 * 5.4 Proof rules for equality
 * 5.5 Interpreting signatures
 * 5.6 Closed terms and sentences
 * 5.7 Satisfaction
 * 5.8 Diophantine sets and relations
 * 5.9 Soundness for qf sentences
 * 5.10 Adequacy and completeness for qf sentences
 * 6 Second interlude: the Linda problem
 * 7 First-order logic
 * 7.1 Quantifiers
 * 7.2 Scope and freedom
 * 7.3 Semantics of first-order logic
 * 7.4 Natural deduction for first-order logic
 * 7.5 Proof and truth in arithmetic
 * 7.6 Soundness and completeness for first-order logic
 * 7.7 First-order theories
 * 7.8 Cardinality
 * 7.9 Things that first-order logic cannot do
 * 8 Postlude
 * Appendix A: The natural deduction rules
 * Appendix B: Denotational semantics
 * Appendix C: Solutions to some exercises
 * Index