Description:
Form 65 (Krein-Milman Theorem) does not imply Form 14 (BPI) in \(ZF^{0}\)
Content:
Form 65 (Krein-Milman Theorem) does not imply Form 14 (BPI) in \(ZF^{0}\). The argument is as follows: By results of Bell/Jellett [1971], Form 14 + Form 65 implies Form 1 (AC). By Pincus [1972b] and Pincus [1972c], Form 65 is true and Form 1 is false in \(\cal N2\) hence Form 14 is false in \(\cal N2\). Similarly, Form 52 does not imply Form 286 in \(ZF\) since Form 52 + Form 286 implies Form 1 (Bell/Jellett [1971]) and by Pincus [1972b], Form 52 does not imply Form 14 in \(ZF\).
Howard-Rubin number: 99
Type: Result