There is No Standard Model of ZFC and 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+ ∃ M ZFC st ), (ii) ¬Con(N F+ ∃ M NF st ), (iii) ¬Con(ZF C 2 ), (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 Read full article: http://bp.bookpi.org/index.php/bpi/catalog/view/46/221/408-1 View Volume: https://doi.org/10.9734/bpi/amacs/v1