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Abstract: In 1993 I. Moerdijk presented a new model of nonstandard arithmetic in the topos of sheaves on a category of filters, Sh($\mathbb{F}$). This was later extended by E. Palmgren to a model of nonstandard analysis. The model in particular makes use of the sheaves ${}^*S$, which at any filter $\mathcal{F}$ is the reduced power of the set $S$ over $\mathcal{F}$, ${}^*S(\mathcal{F})$. The details of this will be given in section 1.3. Before this, in section 1.1, we will give a short background to the... (Update)
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BibTeX entry: (Update)
@misc{ eliasson-ultrapowers,
author = "Jonas Eliasson",
title = "Ultrapowers as Sheaves on a Category of Ultrafilters",
url = "citeseer.ist.psu.edu/eliasson01ultrapowers.html" }
Citations (may not include all citations):10 A model for intuitionistic non-standard arithmetic (context) - Moerdijk - 1995 DBLP
9 Developments in constructive nonstandard analysis (context) - Palmgren - 1998
8 Internal set theory: a new approach to nonstandard analysis (context) - Nelson - 1977
4 A sheaf-theoretic foundation of nonstandard analysis (context) - Palmgren - 1997
2 Two closed categories of filters (context) - Blass - 1977
2 Real numbers in the topos of sheaves over the category of fi.. (context) - Palmgren
2 the category of filters (context) - Koubek, Reiterman - 1970
1 The Rudin-Keisler ordering of P-points (context) - Blass - 1973
1 Keisler Model theory third ed (context) - Chang - 1990
1 Sheaves of structures and generalized ultraproducts (context) - Ellerman - 1974
1 Moerdijk Sheaves in geometry and logic Springer-Verlag (context) - Lane - 1994
1 The syntax of nonstandard analysis (context) - Nelson - 1988
1 Negrepontis The theory of ultrafilters Springer-Verlag (context) - Comfort - 1974
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