Free algebras over Bezout domains are Sylvester domains |
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Authors: | Warren Dicks |
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Affiliation: | Department of Mathematics, Bedford College, London NW1 4NS, England |
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Abstract: | Let λ be a finitary geometric theory and δ its classifying topos. We prove that δ is Boolean if and only if (1) every first-order formula in the language of λ is ?-provably equivalent to a geometric formula and (2) for any finite list of varibles, x, there are, up to ?-provable equivalence, only finitely many formulas, in the language of λ with free variables among x. We use this characterization to show that, when δ is Boolean, it is an atomic topos and can be viewed as a finite coproduct of topoi of continuous G-sets for topological groups G satisfying a certain finiteness condition. |
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Keywords: | 03C35 03G30 18B25 Classifying topos Boolean topos Atomic topos Model-complete theory |
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