Ultrapowers as sheaves on a category of ultrafilters
2004 (English)In: Archive for mathematical logic, ISSN 0933-5846, E-ISSN 1432-0665, Vol. 43, no 7, 825-843 p.Article in journal (Refereed) Published
In the paper we investigate the topos of sheaves on a category of ultrafilters. The category is described with the help of the Rudin-Keisler ordering of ultrafilters. It is shown that the topos is Boolean and two-valued and that the axiom of choice does not hold in it. We prove that the internal logic in the topos does not coincide with that in any of the ultrapowers. We also show that internal set theory, an axiomatic nonstandard set theory, can be modeled in the topos.
Place, publisher, year, edition, pages
2004. Vol. 43, no 7, 825-843 p.
Algebra and Logic
IdentifiersURN: urn:nbn:se:uu:diva-91028DOI: 10.1007/s00153-004-0228-0OAI: oai:DiVA.org:uu-91028DiVA: diva2:163602