Content deleted Content added
m Bot: links syntax |
_algebraic_ distributive lattice |
||
Line 1:
In [[mathematics]], the '''congruence lattice problem''' asks whether every algebraic [[distributive lattice]] is [[isomorphic]] to the congruence lattice of some other lattice. The problem was posed by [[Robert P. Dilworth]], and for many years it was one of the most famous and long-standing open problems in [[lattice theory]]; it had a deep impact on the development of lattice theory itself. The conjecture that every distributive lattice is a congruence lattice is true for all distributive lattices with at most [[Aleph number|ℵ<sub>1</sub>]] [[compact element]]s, but F. Wehrung provided a counterexample for distributive lattices with ℵ<sub>2</sub> compact elements using a construction based on [[Kuratowski's free set theorem]].
==Preliminaries==
| |||