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Various forms of infinity for finitely supported structures

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Abstract

The goal of this paper is to define and study the notion of infinity in the framework of finitely supported structures, presenting new properties of infinite cardinalities. Some of these properties are extended from the non-atomic Zermelo–Fraenkel set theory to the world of atomic objects with finite support, while other properties are specific to finitely supported structures. We compare alternative definitions for infinity in the world of finitely supported sets, and provide relevant examples of atomic sets which satisfy some forms of infinity, while do not satisfy others. Finally, we provide a characterization of finitely supported countable sets.

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Acknowledgements

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

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Authors and Affiliations

  1. Romanian Academy, Institute of Computer Science, Iaşi, Romania

    Andrei Alexandru

  2. Alexandru Ioan Cuza University, Iaşi, Romania

    Gabriel Ciobanu

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  1. Andrei Alexandru
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  2. Gabriel Ciobanu
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Correspondence to Gabriel Ciobanu.

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Alexandru, A., Ciobanu, G. Various forms of infinity for finitely supported structures. Arch. Math. Logic 61, 173–222 (2022). https://doi.org/10.1007/s00153-021-00787-2

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  • DOI: https://doi.org/10.1007/s00153-021-00787-2

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