The Skolem-löwenheim theorem in toposes. II

Studia Logica 44 (1):25 - 38 (1985)

Abstract
This paper is a continuation of the investigation from [13]. The main theorem states that the general and the existential quantifiers are (, -reducible in some Grothendieck toposes. Using this result and Theorems 4.1, 4.2 [13] we get the downward Skolem-Löwenheim theorem for semantics in these toposes.
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DOI 10.1007/BF00370808
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Sheaves and Boolean Valued Model Theory.George Loullis - 1979 - Journal of Symbolic Logic 44 (2):153-183.
The Skolem-Löwenheim Theorem in Toposes.Marek Zawadowski - 1983 - Studia Logica 42 (4):461 - 475.

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