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arXiv:math/0509245math.LO

Analysis in J_2

Nik Weaver

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Abstract

This is an expository paper in which I explain how core mathematics, particularly abstract analysis, can be developed within a concrete countable set J_2 (the second set in Jensen's constructible hierarchy). The implication, well-known to proof theorists but probably not to most mainstream mathematicians, is that ordinary mathematical practice does not require an enigmatic metaphysical universe of sets. I go further and argue that J_2 is a superior setting for normal mathematics because it is free of irrelevant set-theoretic pathologies and permits stronger formulations of existence results.

arXiv comments
31 pages
Journal reference
DOI
Subjects
math.LOLogic math.FAFunctional Analysis math.GMGeneral Mathematics math.HOHistory and Overview

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Linked by 1 identifiable commenter in 2 comments across 2 threads, from Jul 2013 to Aug 2015.

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Discussed in comments2 threads

  1. The Banach–Tarski Paradox [video] 1 comment

    • There's even an argument that separability is sufficient for most of mathematics let alone physics (http://arxiv.org/pdf/math/0509245.pdf) but you're going to have to work very hard to persuade me that if we're going to describe any sets as physical then uncountable ones are…

      tomeView on HNParent context

  2. Indescribable numbers: The theorem that made me fall in love with math 1 comment

    • I'm afraid I'm not a good enough logician to answer your objection properly, but there are, I believe, credible approaches to doing mathematics on a countable carrier set, for example: http://arxiv.org/pdf/math/0509245

      tomeView on HNParent context

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