There is No Standard Model of ZFC and ZFC2
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ZFC2 | Chapter 03 | Advances in Mathematics and Computer Science Vol. 1
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+∃MZF Cst),
(ii)¬Con(N F+∃MNFst),
(iii)¬Con(ZF C2),
(iv) letkbe 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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