## Martin Goldstern, Lukas D. KlausnerStranger things about forcing without AC

Comment.Math.Univ.Carolin. 61,1 (2020) 21-26.

Abstract:Typically, set theorists reason about forcing constructions in the context of Zermelo--Fraenkel set theory (ZFC). We show that without the axiom of choice (AC), several simple properties of forcing posets fail to hold, one of which answers Miller's question from the work: Arnold W.\ Miller, {\it Long Borel hierarchies}, MLQ Math. Log. Q. {\bf 54} (2008), no. 3, 307--322.

Keywords: forcing; axiom of choice; non-AC forcing; ZF

DOI: DOI 10.14712/1213-7243.2020.013
AMS Subject Classification: 03E25 03E40

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