Model Theory of Ultrafinitism I: Fuzzy Initial Segments of Arithmetics

Details Model Theory of Ultrafinitism I: Fuzzy Initial Segments of Arithmetics Model Theory of Ultrafinitism I: Fuzzy Initial Segments of Arithmetics

2006-11-21

arxiv.org/abs/cs/0611100v1

Computer Science

Logic in Computer Science

31 pages, Tennenbaum Memorial invited talk

Scientific paper

This article is the first of an intended series of works on the model theory of Ultrafinitism. It is roughly divided into two parts. The first one addresses some of the issues related to ultrafinitistic programs, as well as some of the core ideas proposed thus far. The second part of the paper presents a model of ultrafinitistic arithmetics based on the notion of fuzzy initial segments of the standard natural numbers series. We also introduce a proof theory and a semantics for ultrafinitism through which feasibly consistent theories can be treated on the same footing as their classically consistent counterparts. We conclude with a brief sketch of a foundational program, that aims at reproducing the transfinite within the finite realm.

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