Processing math: 100%

Description:

Form 62 (C(,<0)) + Form 57 implies Form 9 is not provable in ZF.

Content:

Sageev [1981] shows that the implication Form 62 (C(,<0)) + Form 57 (Any two Dedekind cardinals are comparable) implies Form 9 (Dedekind finite= finite) is not provable in ZF.  Ellentuck [1974] shows that

ZF ( 62 + 57 ω,,+ is an elementary  submodel  of Δ,,+)
where Δ is the set of Dedekind finite cardinals (ωΔ) and  and + are the usual cardinal operations.

Howard-Rubin number: 44

Type: Summary

Back