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Results tagged with axioms
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user 109573
12
votes
Accepted
Is this set theory equivalent to ZFC?
Without this convention, then it's not clear we can prove the existence of $\{x\}$ from the axioms I specified. … Of course, we can prove it exists from Separation and Power Set, which is included in the axioms listed in the question, but that feels overpowered for our purposes. …
- 4,316
12
votes
Accepted
Is every set being cardinal definable consistent with ZF + negation of Choice?
This is consistent. Kanovei constructed a model $M$ with an infinite Dedekind finite set of reals which is lightface projectively definable. By descending to $L(R),$ we can further assume it satisfies …
- 4,316