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Corpus ID: 1144512

A Permutation Model with Finite Partitions of the Set of Atoms as Supports

@article{Bruce2016APM,
title={A Permutation Model with Finite Partitions of the Set of Atoms as Supports},
author={Benjamin Bruce},
journal={Rose–Hulman Undergraduate Mathematics Journal},
year={2016},
volume={17},
pages={4}
}

The method of permutation models was introduced by Fraenkel in 1922 to prove the independence of the axiom of choice in set theory with atoms. We present a variant of the basic Fraenkel model in which supports are finite partitions of the set of atoms, rather than finite sets of atoms. Among our results are that, in this model, every well-ordered family of well-orderable sets has a choice function and that the union of such a family is well-orderable. Acknowledgements: This research was… Expand

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… Expand

We propose that failures of the axiom of choice, that is, surjective functions admitting no sections, can be reasonably classified by means of invariants borrowed from algebraic topology. We show… Expand

Throughout this paper Q will denote an infinite set, S:= Sym(Q) and G is a subgroup of S, and working in ZFC, set theory with Axiom of Choice (AC), the subgroups G with S : G < 2 are sought.Expand

Numerical list of forms Topical list of forms Models Notes References for relations between forms Bibliography Table 1 and Table 2 Subject index Author index Software.