Accession Number : AD0653298

Title :   THE DEFINABILITY OF CARDINAL NUMBERS.

Descriptive Note : Technical rept.,

Corporate Author : HEBREW UNIV JERUSALEM (ISRAEL)

Personal Author(s) : Levy,Azriel

Report Date : MAR 1967

Pagination or Media Count : 44

Abstract : Cardinal numbers are known to be definable in set theory with the axiom of choice or with the axiom of foundation. In the absence of these two axioms the notion of a cardinal number is shown to be undefinable in ZF, in several strong senses. The proofs use models of the Fraenkel-Mostowski type.

Descriptors :   (*SET THEORY, THEOREMS), (*MODEL THEORY, *MAPPING(TRANSFORMATIONS)), SYMBOLS, ISRAEL, METAMATHEMATICS, CALCULUS OF VARIATIONS, LANGUAGE, THEOREMS, MATHEMATICAL MODELS

Subject Categories : Linguistics
      Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE