Geodesic
Stranger things about forcing without AC
Commentationes Mathematicae Universitatis Carolinae, Tome 61 (2020) no. 1, pp. 21-26.

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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, {Long Borel hierarchies}, MLQ Math. Log. Q. {54} (2008), no. 3, 307--322.
DOI : 10.14712/1213-7243.2020.013
Classification : 03E25, 03E40
Keywords: forcing; axiom of choice; non-AC forcing; ZF 
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Goldstern, Martin; Klausner, Lukas D. Stranger things about forcing without AC. Commentationes Mathematicae Universitatis Carolinae, Tome 61 (2020) no. 1, pp. 21-26. doi : 10.14712/1213-7243.2020.013. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2020.013/

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