• 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}
}
  • Benjamin Bruce
  • Published 2016
  • Mathematics
  • Rose–Hulman Undergraduate Mathematics Journal
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… 
1 Citations
Partition models, Permutations of infinite sets without fixed points, Variants of CAC, and weak forms of AC
  • Amitayu Banerjee
  • Mathematics
  • 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

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