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Published in:
2016 | OriginalPaper | Chapter
Fraenkel-Mostowski Set Theory: A Framework for Finitely Supported Mathematics
Authors : Andrei Alexandru, Gabriel Ciobanu
Published in: Finitely Supported Mathematics
Publisher: Springer International Publishing
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In this chapter we present the basics of the Fraenkel-Mostowski framework, by studying concepts like invariant set, Fraenkel-Mostowski set, freshness quantifier, support, finiteness, fresh element, and abstraction. We also prove some original results regarding the consistency of various forms of choice in Finitely Supported Mathematics. Another goal of this chapter is to establish a connection between the theory of Fraenkel-Mostowski sets and the concept of logical notion presented by A. Tarski. More precisely, we prove that any invariant set from the Fraenkel-Mostowski universe is a logical notion in Tarski’s view. Moreover, the freshness quantifier is a logical symbol.