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- W3014843430 abstract "For every univariate formula $$chi $$ (i.e., containing at most one atomic proposition) we introduce a lattice of intermediate theories: the lattice of $$chi $$ -logics. The key idea to define $$chi $$ -logics is to interpret atomic propositions as fixpoints of the formula $$chi ^2$$ , which can be characterised syntactically using Ruitenburg’s theorem. We show that $$chi $$ -logics form a lattice, dually isomorphic to a special class of varieties of Heyting algebras. This approach allows us to build and describe five distinct lattices—corresponding to the possible fixpoints of univariate formulas—among which the lattice of negative variants of intermediate logics." @default.
- W3014843430 created "2020-04-10" @default.
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- W3014843430 date "2022-01-01" @default.
- W3014843430 modified "2023-10-17" @default.
- W3014843430 title "Lattices of Intermediate Theories via Ruitenburg’s Theorem" @default.
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- W3014843430 doi "https://doi.org/10.1007/978-3-030-98479-3_15" @default.
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