Theory of Semisets (eBook)

Front Cover 1
The Theory of Semisets 4
Copyright Page 5
Contents 6
Introduction 8
CHAPTER I. 16
SECTION 1. THE THEORY OF CLASSES 16
SECTION 2. LOGICAL FOUNDATIONS 32
SECTION 3. THE THEORY OF CLASSES CONTINUED 56
SECTION 4. THE THEORY OF SEMISETS 70
CHAPTER II. 90
SECTION 1. ORDINAL NUMBERS 90
SECTION 2. EQUIVALENCE AND SUBVALENCE OF SETS CARDINAL NUMBERS
SECTION 3. THE FIRST AXIOM OF CHOICE 111
SECTION 4. COMPLETE BOOLEAN ALGEBRAS 118
SECTION 5. ORDERED AND SEPARATIVELY ORDERED SETS 130
CHAPTER III. 140
SECTION 1. THE SECOND AND THIRD AXIOMS OF REGULARITY THE SECOND AXIOM OF CHOICE. AXIOMS CONCERNING URELEMENTS
SECTION 2. MODEL-CLASSES AND SET-UNIVERSAL RELATIONS. INDEPENDENCE OF AXIOM (D3) 155
SECTION 3. SYMMETRIC SETS AND THE INDEPENDENCE OF AXIOM (E1) IN TSS' 167
SECTION 4. DEFINABLE SETS AND THE CONSISTENCY OF THE AXIOM OF CHOICE (E2) THE THIRD AXIOM OF CHOICE
SECTION 5. CONSTRUCTIBLE SETS AND THE AXIOM OF CONSTRUCTIBILITY. THE CONSISTENCY OF THE AXIOMS (E3) AND (CONT) 192
CHAPTER IV. 201
SECTION 1. AXIOMS OF SUPPORT 201
SECTION 2. BOOLEAN SUPPORTS 211
SECTION 3. PROPERTIES OF COMPLETE ULTRAFILTERS 228
CHAPTER V. 236
SECTION 1. THE FULL UPWARD EXTENSION OF THE UNIVERSE 236
SECTION 2. THE ULTRAPRODUCT MODEL 253
SECTION 3. CHARACTERISTICS OF COMPLETE BOOLEAN ALGEBRAS AND PROPERTIES OF RELATIONS AND FUNCTIONS 262
CHAPTER VI. 275
SECTION 1. INDEPENDENCE OF THE AXIOM OF CONTINUUM 275
SECTION 2. INDEPENDENCE OF THE AXIOM OF CHOICE 286
SECTION 3. SUPPORT OF ONE MODEL-CLASS OVER ANOTHER 296
SECTION 4. BOOLEAN VALUES AND FORCING 311
BIBLIOGRAPHY 325
INDEX 327
INDEX OF SYMBOLS 331