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. An posible generalization of Lob’s theorem is considered.Main results are: (i)
Con
ZFC 
Mst ZFC, (ii)
Con
ZF 
V  L, (iii)
Con
NF 
Mst NF, (iv)
Con
ZFC2, (v) let k be inaccessible cardinal then
Con
ZFC 

.