Authors: Jaykov Foukzon
In this article we derived an importent example of the inconsistent countable set in second order ZFC (ZFC_2)with the full second-order semantics. Main results is:(i) ~Con(ZFC_2),(ii) let k be an inaccessible cardinal and H_k is a set of all sets having hereditary size less then k, then ~Con(ZFC+V=H_k).
Comments: 22 Pages.
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