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Main Steps in Defining Finitely Supported Mathematics

  • Andrei Alexandru
  • Gabriel CiobanuEmail author
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 594)

Abstract

This paper presents the main steps in defining a Finitely Supported Mathematics by using sets with atoms. Such a mathematics generalizes the classical Zermelo-Fraenkel mathematics, and represents an appropriate framework to work with (infinite) structures in terms of finitely supported objects. We focus on the techniques of translating the Zermelo-Fraenkel results into this Finitely Supported Mathematics over infinite (possibly non-countable) sets with atoms. Two general methods of proving the finite support property for certain algebraic structures are presented. Finally, we provide a survey on the applications of the Finitely Supported Mathematics in experimental sciences.

Keywords

Fraenkel-Mostowski set theory Invariant sets Finite support principle Finitely Supported Mathematics 

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Romanian Academy, Institute of Computer ScienceIaşiRomania

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