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- W1761187662 abstract "The Gratzer-Schmidt theorem of lattice theory states that each algebraic lattice is isomorphic to the congruence lattice of an algebra. We study the reverse mathematics of this theorem. We also show that the set of indices of computable lattices that are complete is $Pi^1_1$-complete; the set of indices of computable lattices that are algebraic is $Pi^1_1$-complete; the set of compact elements of a computable lattice is $Pi^{1}_{1}$ and can be $Pi^1_1$-complete; and the set of compact elements of a distributive computable lattice is $Pi^{0}_{3}$, and there is an algebraic distributive computable lattice such that the set of its compact elements is $Pi^0_3$-complete." @default.
- W1761187662 created "2016-06-24" @default.
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- W1761187662 date "2009-01-01" @default.
- W1761187662 modified "2023-09-24" @default.
- W1761187662 title "The Strength of the Grätzer-Schmidt Theorem" @default.
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- W1761187662 doi "https://doi.org/10.1007/978-3-642-03073-4_7" @default.
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