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• W2083134633 abstract "We introduce infinitary propositional theories over a set and their models which are subsets of the set, and define a generalized geometric theory as an infinitary propositional theory of a special form. The main result is that the class of models of a generalized geometric theory is set-generated . Here, a class $mathcal{X}$ of subsets of a set is set-generated if there exists a subset G of $mathcal{X}$ such that for each α ∈ $mathcal{X}$ , and finitely enumerable subset τ of α there exists a subset β ∈ G such that τ ⊆ β ⊆ α. We show the main result in the constructive Zermelo–Fraenkel set theory ( CZF ) with an additional axiom, called the set generation axiom which is derivable in CZF , both from the relativized dependent choice scheme and from a regular extension axiom. We give some applications of the main result to algebra, topology and formal topology." @default.
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• W2083134633 date "2014-11-10" @default.
• W2083134633 modified "2023-09-23" @default.
• W2083134633 title "Generalized geometric theories and set-generated classes" @default.
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• W2083134633 doi "https://doi.org/10.1017/s0960129513000236" @default.
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