On Elementary Theories of GLP-Algebras

Fedor Pakhomov

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arXiv · 1412.4439

On Elementary Theories of GLP-Algebras

Fedor Pakhomov

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Abstract

There is a polymodal provability logic $GLP$. We consider generalizations of this logic: the logics $GLP_{\alpha}$, where $\alpha$ ranges over linear ordered sets and play the role of the set of indexes of modalities. We consider the varieties of modal algebras that corresponds to the polymodal logics. We prove that the elementary theories of the free $\emptyset$-generated $GLP_{n}$ -algebras are decidable for all finite ordinals $n$.

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Fedor Pakhomov. 2014-12-15. On Elementary Theories of GLP-Algebras. https://arxiv.org/abs/1412.4439

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