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• # Artykuł - szczegóły

## Fundamenta Mathematicae

2008 | 198 | 3 | 217-228

## Free trees and the optimal bound in Wehrung's theorem

EN

### Abstrakty

EN
We prove that there is a distributive (∨,0,1)-semilattice 𝒢 of size ℵ₂ such that there is no weakly distributive (∨,0)-homomorphism from $Con_{c}A$ to 𝒢 with 1 in its range, for any algebra A with either a congruence-compatible structure of a (∨,1)-semi-lattice or a congruence-compatible structure of a lattice. In particular, 𝒢 is not isomorphic to the (∨,0)-semilattice of compact congruences of any lattice. This improves Wehrung's solution of Dilworth's Congruence Lattice Problem, by giving the best cardinality bound possible. The main ingredient of our proof is the modification of Kuratowski's Free Set Theorem, which involves what we call free trees.

217-228

wydano
2008

### Twórcy

autor
• Department of Algebra, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic