Lattices of theories

Details Lattices of theories Lattices of theories

2009-05-04

arxiv.org/abs/0905.0299v1

Mathematics

Category Theory

84 pages

Scientific paper

We show that there is a bijection between the subtoposes of the classifying topos of a geometric theory T over a signature L and the closed geometric theories over L which are `quotients' of the theory T; next, we analyze how classical topos-theoretic constructions on the lattice of subtoposes of a given topos can be transferred, via the bijection above, to logical constructions in the corresponding lattice of theories.

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