Abstract
We shall develop a duality for the category finitely presented Heyting algebras H A fp . Using a combinatorial description M H of H A op fp we shall prove that it is a Heyting category and hence, according to Theorem 3.8, the theory of Heyting algebras T H admits a model completion T * H . Then we shall study some further properties of H A op fp and we shall derive some conclusions from these studies for intuitionistic propositional logic IpC. We introduce a sheaf semantics for second order logic and show how to use it to eliminate quantifiers in T * H .
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© 2002 Springer Science+Business Media Dordrecht
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Ghilardi, S., Zawadowski, M. (2002). Heyting Algebras. In: Sheaves, Games, and Model Completions. Trends in Logic, vol 14. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9936-8_4
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DOI: https://doi.org/10.1007/978-94-015-9936-8_4
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-6036-5
Online ISBN: 978-94-015-9936-8
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