There is No Standard Model of ZFC and ZFC_2 with Henkin semantics.Generalized Lob's Theorem.Strong Reflection Principles and Large Cardinal Axioms.Consistency Results in Topology

Abstract

In this article we proved so-called strong reflection principles corresponding to formal theories Th which has omega-models. An posible generalization of the Lob's theorem is considered.Main results is: (1) let $k$ be an inaccessible cardinal, then $\neg Con(ZFC+\exists k)$,(2) there is a Lindel\"of $T_3$ indestructible space of pseudocharacter $\leqslant \aleph_1$ and size $\aleph_2$ in $L$.