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Inconsistent Countable Set in Second Order ZFC and Nonexistence of the Strongly Inaccessible Cardinals

Jaykov Foukzon

Journal of Advances in Mathematics and Computer Science · pp. 380–393 · Published 6 Jun 2015

10.9734/BJMCS/2015/16849

Abstract

In this article we derived an important example of the inconsistent countable set in second order ZFC (ZFC2) with the full second-order semantics. Main results: (i) ¬Con(ZFC2), (ii) let k be an inaccessible cardinal and Hk is a set of all sets having hereditary size less then k, then ¬Con(ZFC + (V = Hk)).

Gödel encoding Completion of ZFC2 Russell′ s paradox ω-model Henkin semantics full second-order semantics.

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