The strength of the Graetzer-Schmidt theorem

(ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image).The Graetzer-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 that1.the set of indices...

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Bibliographic Details
Published in:Archive for mathematical logic 2016-08, Vol.55 (5-6), p.687-704
Main Authors: Brodhead, Katie, Khan, Mushfeq, Kjos-Hanssen, Bjoern, Lampe, William A, Nguyen, Paul Kim Long V, Shore, Richard A
Format: Article
Language:English
Subjects:
Algebra
Archives
Congruences
Lattices
Mathematical logic
Mathematical models
Texts
Theorems
Online Access:Get full text
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Summary:(ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image).The Graetzer-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 that1.the set of indices of computable lattices that are complete is ...-complete; 2.the set of indices of computable lattices that are algebraic is ...-complete; 3.the set of compact elements of a computable lattice is ... and can be ...-complete; and4.the set of compact elements of a distributive computable lattice is ..., and there is an algebraic distributive computable lattice such that the set of its compact elements is ...-complete.
ISSN:0933-5846
1432-0665
DOI:10.1007/s00153-016-0488-5