Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lattices of Intermediate Theories via Ruitenburg's Theorem   For every univariate formula $\chi$ we introduce a lattices 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 develop an
algebraic duality between the lattice of $\chi$-logics and a special class of
varieties of Heyting algebras. This approach allows us to build five distinct
lattices corresponding to the possible fixpoints of univariate formulas|among
which the lattice of negative variants of intermediate logics. We describe
these lattices in more detail.

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The categories of this paper are: supr-con
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The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
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The categories of this paper are: plasm-ph
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The categories of this paper are: math-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
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The categories of this paper are: chao-dyn
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The categories of this paper are: gr-qc
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The categories of this paper are: mtrl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: stat
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The categories of this paper are: nlin