《SET THEORY AND ITS LOGIC》求取 ⇩

INTRODUCTION1

Part One．The Elements7

Ⅰ．LOGIC9

1．Quantification and identity9

2．Virtual classes15

3．Virtual relations21

Ⅱ．REAL CLASSES28

4．Reality，extensionality，and the individual28

5．The virtual amid the real34

6．Identity and substitution40

Ⅲ．CLASSES OF CLASSES47

7．Unit classes47

8．Unions，intersections，descriptions53

9．Relations as classes of pairs58

10．Functions65

Ⅳ．NATURAL NUMBERS74

11．Numbers unconstrued74

12．Numbers construed81

13．Induction86

Ⅴ．ITERATION AND ARITHMETIC95

14．Sequences and iterates95

15．The ancestral100

16．Sum，product，power106

Part Two．Higher Forms of Number117

Ⅵ．REAL NUMBERS119

17．Program．Numerical pairs119

18．Ratios and reals construed124

19．Existential needs．Operations and extensions130

Ⅶ．ORDER AND ORDINALS139

20．Transfinite induction139

21．Order145

22．Ordinal numbers150

23．Laws of ordinals158

24．Their well-ordering and some consequences165

Ⅷ．TRANSFINITE RECURSION171

25．Transfinite recursion171

26．Laws of transfinite recursion177

27．Enumeration184

Ⅸ．CARDINAL NUMBERS193

28．Comparative size of classes193

29．The Schroder-Bernstein theorem203

30．Infinite cardinal numbers208

Ⅹ．THE AXIOM OF CHOICE217

31．Selections and selectors217

32．Further equivalents of the axiom224

33．The place of the axiom231

Part Three．Axiomatic Theories239

Ⅸ．RUSSELL＇S THEORY OF TYPES241

34．The constructive part241

35．Classes and the axiom of reducibility249

36．The modern theory of types259

Ⅻ．GENERAL VARIABLES AND ZERMELO266

37．The theory of types with general variables266

38．Cumulative types and Zermelo272

39．Axioms of infinity and others279

ⅩⅢ．STRATIFICATION AND ULTIMATE CLASSES287

40．＂New foundations＂287

41．Non-Cantorian classes．Induction again292

42．Ultimate classes added299

ⅩⅣ．VON NEUMANN＇S SYSTEM AND OTHERS310

43．The von Neumann-Bernays system310

44．Departures and comparisons315

45．Strength of systems323

SYNOPSIS OF FIVE AXIOM SYSTEMS331

LIST OF NUMBERED FORMULAS333

BIBLIOGRAPHICAL REFERENCES343

INDEX351