Publisher： Cambridge University Press
E-ISSN： 1943-5886|48|2|263-287
ISSN： 0022-4812
Source： The Journal of Symbolic Logic, Vol.48, Iss.2, 1983-06, pp. : 263-287
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Abstract
The incompleteness of ZF set theory leads one to look for natural extensions of ZF in which one can prove statements independent of ZF which appear to be “true”. One approach has been to add large cardinal axioms. Or, one can investigate second-order expansions like Kelley-Morse class theory, KM. In this paper we look at a set theory ZF(aa), with an added quantifier aa which ranges over ordinals. The “aa” stands for “almost all”, and although we will consider interpretations in terms of the closed unbounded filter on a regular cardinal κ, we will consider other interpretations also.
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