Abstract
The Grätzer-Schmidt theorem of lattice theory states that each algebraic lattice is isomorphic to the congruence lattice of an algebra. A lattice is algebraic if it is complete and generated by its compact elements. We show that the set of indices of computable lattices that are complete is π11-complete; the set of indices of computable lattices that are algebraic is π11-complete; and that there is a computable lattice L such that the set of compact elements of L is π11-complete. As a corollary, there is a computable algebraic lattice that is not computably isomorphic to any computable congruence lattice. © 2009 Springer Berlin Heidelberg.
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CITATION STYLE
Brodhead, P., & Kjos-Hanssen, B. (2009). The strength of the Grätzer-Schmidt theorem. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5635 LNCS, pp. 59–67). https://doi.org/10.1007/978-3-642-03073-4_7
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