Abstract
We study two sheaf representations of elementary toposes, by drawing two different analogies between topos theory and ring theory. When the Heyting algebra of subobjects of 1 is Boolean, the two representations coincide. In particular, when the topos satisfies the axiom of choice, this sheaf representation comprises Henkin's completeness theorem for type theory, the stalks of the sheaf being his general models.
| Original language | English |
|---|---|
| Pages (from-to) | 275-295 |
| Number of pages | 21 |
| Journal | Studies in Logic and the Foundations of Mathematics |
| Volume | 110 |
| Issue number | C |
| DOIs | |
| Publication status | Published - 1 Jan 1982 |
Bibliographical note
Funding Information:One of these sheaf representations was first presented at the Columbia Topos meeting in December 1980. Both authors had support from the National Science and Engineering Research Council of Canada, the senior author also from the Humanities and Social Science Research Council of Canada, moreover he shared a grant from the Quebec Department of Education.
Funding
One of these sheaf representations was first presented at the Columbia Topos meeting in December 1980. Both authors had support from the National Science and Engineering Research Council of Canada, the senior author also from the Humanities and Social Science Research Council of Canada, moreover he shared a grant from the Quebec Department of Education.