The Consistency of the Axiom of Choice and of the Generalized Continuum-hypothesis with the Axioms of Set TheoryPrinceton University Press, 1940 - 66 pages |
Table des matières
THE AXIOMS OF ABSTRACT SET THEORY | 3 |
EXISTENCE OF CLASSES AND SETS | 8 |
ORDINAL NUMBERS | 21 |
CARDINAL NUMBERS | 30 |
THE MODEL | 35 |
PROOF OF THE AXIOMS OF GROUPS AD FOR THE MODEL A | 45 |
PROOF THAT V L HOLDS IN THE MODEL | 47 |
PROOF THAT V L IMPLIES THE AXIOM OF CHOICE AND THE GENERALISED CONTINUUMHYPOTHESIS | 53 |
APPENDIX | 62 |
Special Symbols | 63 |
65 | |
Notes added to the second printing | 67 |
Autres éditions - Tout afficher
The Consistency of the Axiom of Choice and of the Generalized Continuum ... Kurt Gödel Affichage d'extraits - 1966 |
The Consistency of the Axiom of Choice and of the Generalized Continuum ... Kurt Gödel Affichage d'extraits - 1951 |
Expressions et termes fréquents
absolute assume axiom A2 axiom of choice axiom of extensionality axioms of groups axioms of infinity Bernays bound variables called cardinal CHAPTER class of ordinal classes and sets closed with respect Comp concepts Consider constructible classes constructible set defining postulate denoted domain E-section element equivalent existence theorem ɛ-relation following theorem follows immediately generalised continuum-hypothesis Hence the theorem holds iaß implies inductive hypothesis integers isomorphism with respect J₁ logical operators Mar{aß Math metamathematical Neumann Notes added notions and operations obtained On² ordered pair ordered triple ordinal number P₂ Pr(X Proof proper class properties propositional function R-section relativised axioms relativised postulate replaced satisfies the condition satisfies the relativised second printing set of ordinals set theory Similarly smallest ordinal special classes subset Suppose term tion transfinite induction triadic relations uɛX uɛY Un(X well-ordering