4.1 Article

Extensions of Solovay's system S without independent sets of axioms

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ANNALS OF PURE AND APPLIED LOGIC
卷 175, 期 1, 页码 -

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ELSEVIER
DOI: 10.1016/j.apal.2023.103360

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Quasi -normal modal logic; Independent axiomatizability; Lattices of logics

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This paper solves the problem of the existence of extensions of Solovay's system S that do not admit deductively independent sets of axioms by exhibiting countably many extensions of S without deductively independent sets of axioms.
Chagrov and Zakharyaschev posed the problem of existence of extensions of Solovay's system S, which is a non-normalizable quasi-normal modal logic, that do not admit deductively independent sets of axioms. This paper gives a solution by exhibiting countably many extensions of S without deductively independent sets of axioms.(c) 2023 Elsevier B.V. All rights reserved.

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