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Realism, nonstandard set theory, and large cardinals

✍ Scribed by Karel Hrbacek

Book ID: 104307114
Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 244 KB
Volume: 109
Category: Article
ISSN: 0168-0072
DOI: 10.1016/s0168-0072(01)00039-2

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✦ Synopsis

Mathematicians justify axioms of set theory "intrinsically", by reference to the universe of sets of their intuition, and "extrinsically", for example, by considerations of simplicity or usefullness for mathematical practice. Here we apply the same kind of justiÿcations to Nonstandard Analysis and argue for acceptance of BNST + (Basic Nonstandard Set Theory plus additional Idealization axioms). BNST + has nontrivial consequences for standard set theory; for example, it implies existence of inner models with measurable cardinals. We also consider how to practice Nonstandard Analysis in BNST + ; and compare it with other existing nonstandard set theories.

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