Endre søk
RefereraExporteraLink to record
Permanent link

Direct link
Referera
Referensformat
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Annet format
Fler format
Språk
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Annet språk
Fler språk
Utmatningsformat
  • html
  • text
  • asciidoc
  • rtf
Ultrasheaves and double negation
Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
2004 (engelsk)Inngår i: Notre Dame Journal of Formal Logic, ISSN 0029-4527, E-ISSN 1939-0726, Vol. 45, nr 4, s. 235-245Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

Moerdijk has introduced a topos of sheaves on a category of filters. Following his suggestion, we prove that its double negation subtopos is the topos of sheaves on the subcategory of ultrafilters—the ultrasheaves. We then use this result to establish a double negation translation of results between the topos of ultrasheaves and the topos on filters.

sted, utgiver, år, opplag, sider
2004. Vol. 45, nr 4, s. 235-245
HSV kategori
Identifikatorer
URN: urn:nbn:se:uu:diva-91029DOI: 10.1305/ndjfl/1099238447OAI: oai:DiVA.org:uu-91029DiVA, id: diva2:163603
Tilgjengelig fra: 2003-11-25 Laget: 2003-11-25 Sist oppdatert: 2017-12-14bibliografisk kontrollert
Inngår i avhandling
1. Ultrasheaves
Åpne denne publikasjonen i ny fane eller vindu >>Ultrasheaves
2003 (engelsk)Doktoravhandling, med artikler (Annet vitenskapelig)
Abstract [en]

This thesis treats ultrasheaves, sheaves on the category of ultrafilters.

In the classical theory of ultrapowers, you start with an ultrafilter and, given a structure, you construct the ultrapower of the structure over the ultrafilter. The fundamental result is Los's theorem for ultrapowers giving the connection between what formulas are satisfied in the ultrapower and in the original structure. In this thesis we instead start with the category of ultrafilters (denoted U). On this category U we build the topos of sheaves on U (the ultrasheaves), which we think of as generalized ultrapowers.

The theorem for ultrapowers corresponding to Los's theorem is Moerdijk's theorem, first proved by Moerdijk for the topos Sh(F) of sheaves on filters. In the thesis we prove that Los's theorem follows from Moerdijk's theorem. We also investigate the exact relation between the topos of ultrasheaves and Moerdijk's topos Sh(F) and prove that Sh(U) is the double negation subtopos of Sh(F).

The connection between ultrapowers and ultrasheaves is investigated in detail. We also prove some model theoretic results for ultrasheaves, for instance we prove that they are saturated models. The Rudin-Keisler ordering is a tool used in set theory to study ultrafilters. It has a strong relationship to the category U. Blass has given a model theoretic characterization of this ordering and in the thesis we give a new proof of his result.

One common use of ultrapowers is to give non-standard models. In the thesis we prove that you can model internal set theory (IST) in the ultrasheaves. IST, introduced by Nelson, is a non-standard set theory, an axiomatic approach to non-standard mathematics.

sted, utgiver, år, opplag, sider
Uppsala: Matematiska institutionen, 2003. s. 54
Serie
Uppsala Dissertations in Mathematics, ISSN 1401-2049 ; 30
Emneord
Logic, symbolic and mathematical, 03G30, 03C20, 03H05, Matematisk logik
HSV kategori
Identifikatorer
urn:nbn:se:uu:diva-3762 (URN)91-506-1716-8 (ISBN)
Disputas
2003-12-18, Room 111, Building 1, Polacksbacken, Uppsala, 13:15
Opponent
Veileder
Tilgjengelig fra: 2003-11-25 Laget: 2003-11-25bibliografisk kontrollert

Open Access i DiVA

Fulltekst mangler i DiVA

Andre lenker

Forlagets fulltekst
Av organisasjonen
I samme tidsskrift
Notre Dame Journal of Formal Logic

Søk utenfor DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric

doi
urn-nbn
Totalt: 571 treff
RefereraExporteraLink to record
Permanent link

Direct link
Referera
Referensformat
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Annet format
Fler format
Språk
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Annet språk
Fler språk
Utmatningsformat
  • html
  • text
  • asciidoc
  • rtf