Abstract
The finite support axiom of Fraenkel-Mostowski set theory is very strong. We study the consequences of replacing this strong axiom with a weaker one. In this chapter we generalize Fraenkel-Mostowski set theory by giving a new set of axioms which defines Extended Fraenkel-Mostowski set theory. In Extended Fraenkel- Mostowski set theory, instead of the finite support axiom we require that each subset of the set of atoms is either finite or cofinite. We study several algebraic, order and topological properties of Extended Fraenkel-Mostowski sets.
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© 2016 Springer International Publishing Switzerland
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Alexandru, A., Ciobanu, G. (2016). Extended Fraenkel-Mostowski Set Theory. In: Finitely Supported Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-42282-4_4
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DOI: https://doi.org/10.1007/978-3-319-42282-4_4
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-42281-7
Online ISBN: 978-3-319-42282-4
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