# Partition models, Permutations of infinite sets without fixed points, Variants of CAC, and weak forms of AC

@inproceedings{Banerjee2021PartitionMP, title={Partition models, Permutations of infinite sets without fixed points, Variants of CAC, and weak forms of AC}, author={Amitayu Banerjee}, year={2021} }

We study new relations of the following statements with weak choice principles in ZF (ZermeloFraenkel set theory without the Axiom of Choice (AC)) and ZFA (ZF with the axiom of extensionality weakened to allow the existence of atoms). • For every infinite set X, there exists a permutation of X without fixed points. • There is no Hausdorff space X such that every infinite subset of X contains an infinite compact subset. • If a field has an algebraic closure then it is unique up to isomorphism…

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