Open AccessCONTRADICTIONS WITHIN ZERMELO–FRAENKEL SET THEORY WITH AXIOM OF CHOICE
Author(s) -
O. Kolos
Publication year - 2020
Publication title -
lógos. mistectvo naukovoï dumki
Language(s) - English
Resource type - Journals
eISSN - 2663-4139
pISSN - 2617-7064
DOI - 10.36074/2663-4139.10.05
Subject(s) - zermelo–fraenkel set theory , axiom of choice , urelement , mathematics , constructive set theory , lemma (botany) , counterexample , set theory , ideal (ethics) , discrete mathematics , choice function , axiom , set (abstract data type) , pure mathematics , mathematical economics , epistemology , computer science , geometry , ecology , philosophy , poaceae , biology , programming language
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.