Properties of the atoms in finitely supported structures

  • Andrei Alexandru
  • Gabriel CiobanuEmail author


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).


Finitely supported sets Atoms Fixed points Choice principles 

Mathematics Subject Classification

03E35 03E10 03B70 



The authors are grateful to an anonymous referee for several comments and suggestions which improve the paper.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Romanian AcademyInstitute of Computer ScienceIaşiRomania
  2. 2.Alexandru Ioan Cuza UniversityIaşiRomania

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