Properties of the atoms in finitely supported structures
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The goal of this paper is to present a collection of properties of the set of atoms and the set of finite injective tuples of atoms, as well as of the (finite and cofinite) powersets of atoms in the framework of finitely supported structures. Some properties of atoms are obtained by translating classical Zermelo–Fraenkel results into the new framework, but several important properties are specific to finitely supported structures (i.e. they do not have related classical Zermelo–Fraenkel and related non-atomic correspondents).
KeywordsFinitely supported sets Atoms Fixed points Choice principles
Mathematics Subject Classification03E35 03E10 03B70
The authors are grateful to an anonymous referee for several comments and suggestions which improve the paper.
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