Introduction to Elementary Mathematical Logic

Author\'s Preface
Contents
INTRODUCTION
1 PROPOSITIONAL LOGIC
	1 OBJECTS AND OPERATIONS
	2 FORMULAS. EQUIVALENT FORMULAS. TAUTOLOGIES
	3 EXAMPLES OF THE APPLICATION OF THE LAWS OF THE LOGIC OF PROPOSITIONS IN DERIVATIONS
	4 NORMAL FORMS OF FUNCTIONS. MINIMAL FORMS
	5 APPLICATION OF THE ALGEBRA OF PROPOSITIONS TO THE SYNTHESIS AND ANALYSIS OF DISCRETE-ACTION NETWORKS
2 THE PROPOSITIONAL CALCULUS
	1 THE AXIOMATIC METHOD. THE CONSTRUCTION OF FORMALIZED LANGUAGES
	2 CONSTRUCTION OF A PROPOSITIONAL CALCULUS (ALPHABET, FORMULAS, DERIVED FORMULAS)
	3 CONSISTENCY, INDEPENDENCE, AND COMPLETENESS OF A SYSTEM OF AXIOMS IN THE PROPOSITIONAL CALCULUS
3 PREDICATE LOGIC
	1 SETS. OPERATIONS ON SETS
	2 THE INADEQUACY OF PROPOSITIONAL LOGIC. PREDICATES
	3 OPERATIONS ON PREDICATES. QUANTIFIERS
	4 FORMULAS OF PREDICATE LOGIC. EQUIVALENT FORMULAS. UNIVERSALLY VALID FORMULAS
	5 TRADITIONAL LOGIC (THE LOGIC OF ONE-PLACE PREDICATES)
	6 PREDICATE LOGIC WITH EQUALITY. AXIOMATIC CONSTRUCTION OF MATHEMATICAL THEORIES IN THE LANGUAGE Of PREDICATE LOGIC WITH EQUALITY
APPENDIXES
	I A PROOF OF THE DUALITY PRINCIPLE FOR PROPOSITIONAL LOGIC
	II A PROOF OF THE DEDUCTION THEOREM FOR THE PROPOSITIONAL CALCULUS
	III A PROOF OF THE COMPLETENESS THEOREM FOR THE PROPOSITIONAL CALCULUS
BIBLIOGRAPHY
INDEX OF SPECIAL SYMBOLS
INDEX