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Erschienen in:
2016 | OriginalPaper | Buchkapitel
Introduction
verfasst von : Andrei Alexandru, Gabriel Ciobanu
Erschienen in: Finitely Supported Mathematics
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We start this chapter by presenting some motivation for using nominal sets and Fraenkel-Mostowski sets in the experimental sciences. We emphasize the subdivisions of the so-called Fraenkel-Mostowski framework by mentioning the Fraenkel-Mostowski permutation model of Zermelo-Fraenkel set theory with atoms, the Fraenkel-Mostowski axiomatic set theory, the theory of nominal sets, the theory of generalized nominal sets, and Extended Fraenkel-Mostowski set theory. Finally, we present an alternative mathematics for managing infinite structures in the experimental sciences. This is called Finitely Supported Mathematics and represents, informally, Zermelo-Fraenkel mathematics rephrased in terms of finitely supported structures.