Notre Dame Journal of Formal Logic

Ultrasheaves and Double Negation

Steve Awodey and Jonas Eliasson

Abstract

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.

Article information

Source
Notre Dame J. Formal Logic, Volume 45, Number 4 (2004), 235-245.

Dates
First available in Project Euclid: 29 October 2004

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1099238447

Digital Object Identifier
doi:10.1305/ndjfl/1099238447

Mathematical Reviews number (MathSciNet)
MR2130480

Zentralblatt MATH identifier
1093.03041

Subjects
Primary: 03G30: Categorical logic, topoi [See also 18B25, 18C05, 18C10]

Keywords
ultrapower Moerdijk's Topos double negation subtopos sheaf theory

Citation

Awodey, Steve; Eliasson, Jonas. Ultrasheaves and Double Negation. Notre Dame J. Formal Logic 45 (2004), no. 4, 235--245. doi:10.1305/ndjfl/1099238447. https://projecteuclid.org/euclid.ndjfl/1099238447


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