Since 2014
Classifying Toposes for First Order Theories
BRICS Report Series
View Archive Info| Field | Value | |
| Title |
Classifying Toposes for First Order Theories
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| Creator |
Butz, Carsten
Johnstone, Peter T. |
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| Description |
By a classifying topos for a first-order theory T, we mean a toposE such that, for any topos F, models of T in F correspond exactly toopen geometric morphisms F ! E. We show that not every (infinitary)first-order theory has a classifying topos in this sense, but wecharacterize those which do by an appropriate `smallness condition',and we show that every Grothendieck topos arises as the classifyingtopos of such a theory. We also show that every first-order theory has a conservative extension to one which possesses a classifying topos, and we obtain a Heyting-valued completeness theorem for infinitary first-order logic.
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| Publisher |
Aarhus University
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| Date |
1997-01-20
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| Type |
info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion |
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| Format |
application/pdf
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| Identifier |
https://tidsskrift.dk/brics/article/view/18946
10.7146/brics.v4i20.18946 |
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| Source |
BRICS Report Series; No 20 (1997): RS-20 Classifying Toposes for First Order Theories
BRICS Report Series; Nr. 20 (1997): RS-20 Classifying Toposes for First Order Theories 1601-5355 0909-0878 |
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| Language |
eng
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| Relation |
https://tidsskrift.dk/brics/article/view/18946/16585
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