CONTRADICTIONS WITHIN ZERMELO–FRAENKEL SET THEORY WITH AXIOM OF CHOICE
O. Kolos · ΛΌГOΣ МИСТЕЦТВО НАУКОВОЇ ДУМКИ · 2020
By using a counterexample to the known equivalent of the axiom of choice (Krull’s theorem about maximal ideal existence) contradictions within Zermelo–Fraenkel set theory with axiom of choice was shown. Ring ideals set which satisfies the Zorn’s lemma conditions, but with no maximal ele-ment was built.