TITLE:
There Is No Standard Model of ZFC and ZFC2 with Henkin Semantics
AUTHORS:
Jaykov Foukzon, Elena Men’kova
KEYWORDS:
Gödel Encoding, Completion of ZFC, Russell’s Paradox, ω-Model, Henkin Semantics, Full Second-Order Semantic, Strongly Inaccessible Cardinal
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.9 No.9,
September
16,
2019
ABSTRACT: In this article we proved so-called strong reflection principles corresponding to formal theories Th which has omega-models or nonstandard model with standard part. A possible generalization of Löb’s theorem is considered. Main results are: 1) , 2) , 3) , 4) , 5) let k be inaccessible cardinal then .