In this Chapter we obtain a contradictions in formal set theories under assumption that these theories have omega-models or nonstandard model with standard part. An possible generalization of Lob’s theorem is considered. Main results are:
(i) ¬Con(ZF C+∃MZFCst),
(ii) ¬Con(N F+∃MNFst),
(iii) ¬Con(ZF C2),
(iv) let k be an inaccessible cardinal then ¬Con(ZF C+∃κ),
(v) ¬Con(ZF C+ (V=L)),
(vi) ¬Con(ZF+ (V=L)).
Author Details:
Jaykov Foukzon
Israel Institute of Technology, Haifa, Israel
Men’kova Elena Romanovna
All-Russian Research Institute for Optical and Physical Measurements, Moscow, Russia
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