THE MATHEMATICS OF LOGIC

By ELIZABETH HERNANDEZ

CONTENTS K¨ONIG’S LEMMA TWO WAYS OF LOOKING AT MATHEMATICS EXAMPLES AND EXERCISES K¨ONIG’S LEMMA AND REVERSE MATHEMATICS* POSETS AND MAXIMAL ELEMENTS INTRODUCTION TO ORDER ZORN’S LEMMA AND THE AXIOM OF CHOICE* FORMAL SYSTEMS POST SYSTEMS AND COMPUTABILITY* DEDUCTIONS IN POSETS PROVING STATEMENTS ABOUT A POSET LINEARLY ORDERING ALGEBRAIC STRUCTURES* BOOLEAN ALGEBRAS BOOLEAN ALGEBRA AND THE ALGEBRA OF BOOLE* PROPOSITIONAL LOGIC A SYSTEM FOR PROOF ABOUT PROPOSITIONS DECIDABILITY OF PROPOSITIONAL LOGIC* VALUATIONS SEMANTICS FOR PROPOSITIONAL LOGIC THE COMPLEXITY OF SATIS?ABILITY* FILTERS AND IDEALS ALGEBRAIC THEORY OF BOOLEAN ALGEBRAS TYCHONOV’S THEOREM* THE STONE REPRESENTATION THEOREM* FIRST-ORDER LOGIC FIRST-ORDER LANGUAGES SECOND- AND HIGHER-ORDER LOGIC* COMPLETENESS AND COMPACTNESS PROOF OF COMPLETENESS AND COMPACTNESS THE COMPACTNESS THEOREM AND TOPOLOGY* THE OMITTING TYPES THEOREM* MODEL THEORY COUNTABLE MODELS AND BEYOND CARDINAL ARITHMETIC* NONSTANDARD ANALYSIS IN?NITESIMAL NUMBERS OVERSPILL AND APPLICATIONS* REFERENCES