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+∃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
View Volume: https://doi.org/10.9734/bpi/amacs/v1
Comments
Post a Comment