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Special completions of semilattices and lattices
 
 
Description:  Canonical extensions of (bounded) lattices have been extensively studied, and the basic existence and uniqueness theorems for these have been extended to general posets. In this talk we will consider profinite completions of semilattices which may be identified with the iterated filter completion via the duality theory available for semilattices. We will show how canonical extensions of semilattices can be obtained from their profinite completions.
Canonical extensions of bounded lattices are brought within this framework by considering semilattice reducts and the links between different available completions of lattices will be referred. Lifting of semilattice morphisms can be considered in any of these settings. This leads to a very transparent proof that a homomorphism between bounded lattices lifts to a complete lattice homomorphism between the canonical extensions.

 

Date:  2013-02-26
Start Time:   15:00
Speaker:  Maria João Gouveia (Univ. Lisboa)
Institution:  Faculdade de Ciências, Universidade de Lisboa
Place:  Sala 5.5
Research Groups: -Algebra, Logic and Topology
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