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

TL;DR

This paper explores strong reflection principles, generalizes Lob's theorem, and presents consistency results in topology, including the existence of specific topological spaces and consistency statements related to large cardinals.

Contribution

It introduces new strong reflection principles for theories with omega-models, generalizes Lob's theorem, and establishes novel consistency results involving large cardinals and topology.

Findings

Negation of the consistency of ZFC with an inaccessible cardinal

Existence of a Lindelöf T3 indestructible space with specific properties in L

Generalization of Lob's theorem to broader contexts

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 $L$.