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...