Intensionality, Reflection, and Large Cardinals
β Scribed by N. V. Belyakin; V. A. Ganov
- Book ID
- 110404534
- Publisher
- SP MAIK Nauka/Interperiodica
- Year
- 2002
- Tongue
- English
- Weight
- 198 KB
- Volume
- 43
- Category
- Article
- ISSN
- 0037-4466
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## Abstract We show that weakly compact cardinals are the smallest large cardinals __k__ where __k__^+^ < __k__^+^ is impossible provided 0^#^ does not exist. We also show that if __k__^+^^Kc^ < __k__^+^ for some __k__ being weakly compact (where K^c^ is the countably complete core model below one
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 justiΓΏcations to Nonstandard Analysis and a