Stranger things about forcing without AC
Martin Goldstern; Lukas D. Klausner
Commentationes Mathematicae Universitatis Carolinae (2020)
- Volume: 61, Issue: 1, page 21-26
- ISSN: 0010-2628
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Abstract
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topGoldstern, Martin, and Klausner, Lukas D.. "Stranger things about forcing without AC." Commentationes Mathematicae Universitatis Carolinae 61.1 (2020): 21-26. <http://eudml.org/doc/297072>.
@article{Goldstern2020,
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, \{Long Borel hierarchies\}, MLQ Math. Log. Q. \{54\} (2008), no. 3, 307--322.},
author = {Goldstern, Martin, Klausner, Lukas D.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {forcing; axiom of choice; non-AC forcing; ZF},
language = {eng},
number = {1},
pages = {21-26},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Stranger things about forcing without AC},
url = {http://eudml.org/doc/297072},
volume = {61},
year = {2020},
}
TY - JOUR
AU - Goldstern, Martin
AU - Klausner, Lukas D.
TI - Stranger things about forcing without AC
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2020
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 61
IS - 1
SP - 21
EP - 26
AB - 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.
LA - eng
KW - forcing; axiom of choice; non-AC forcing; ZF
UR - http://eudml.org/doc/297072
ER -
References
top- Karagila A., Do choice principles in all generic extensions imply AC in ?, Answer to a MathOverflow question, 2018.
- Kunen K., Set Theory: An Introduction to Independence Proofs, Studies in Logic and the Foundations of Mathematics, 102, North-Holland Publishing Co., Amsterdam, 1983. Zbl0534.03026MR0756630
- Miller A. W., 10.1002/malq.200710044, MLQ Math. Log. Q. 54 (2008), no. 3, 307–322. MR2417803DOI10.1002/malq.200710044
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