 
Summary: UPPSALA DISSERTATIONS IN MATHEMATICS
30
Ultrasheaves
Jonas Eliasson
Department of Mathematics
Uppsala University
UPPSALA 2003
Dissertation for the degree of Doctor of Philosophy in mathematical logic presented
at Uppsala University in 2003.
Abstract
Eliasson, J. 2003: Ultrasheaves. Uppsala dissertations in Mathematics 30. 54 pp.
Uppsala. ISBN 9150617168.
This thesis treats ultrasheaves, sheaves on the category of ultrafilters.
In the classical theory of ultrapowers, you start with an ultrafilter (I, U) and,
given a structure S, you construct the ultrapower SI
/U. The fundamental result
is Lo´s's theorem for ultrapowers giving the connection between what formulas are
satisfied in the ultrapower and in the original structure S. In this thesis we instead
start with the category of ultrafilters (denoted U). On this category we build the
topos Sh(U) of sheaves on U (the ultrasheaves), which we think of as generalized
