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arXiv · 1308.1696

An Easton-like Theorem for Zermelo-Fraenkel Set Theory Without Choice (Preliminary Report)

Anne Fernengel·Peter Koepke
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Abstract

By Easton's theorem one can force the exponential function on regular cardinals to take rather arbitrary cardinal values provided monotonicity and Koenig's lemma are respected. In models without choice we employ a "surjective" version of the exponential function. We then prove a choiceless Easton's theorem: one can force the surjective exponential function on all infinite cardinals to take arbitrary cardinal values, provided monotonicity and Cantor's theorem are satisfied, irrespective of cofinalities.

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Anne Fernengel, Peter Koepke. 2013-08-07. An Easton-like Theorem for Zermelo-Fraenkel Set Theory Without Choice (Preliminary Report). https://arxiv.org/abs/1308.1696

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