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Canonical Extensions and Profinite Completions of Semilattices and Lattices

Abstract:

Canonical extensions of (bounded) lattices have been extensively studied, and the basic existence and uniqueness theorems for these have been extended to general posets. This paper focuses on the intermediate class {Mathematical expression} of (unital) meet semilattices. Any {Mathematical expression} embeds into the algebraic closure system Filt(Filt(S)). This iterated filter completion, denoted Filt(S), is a compact and {Mathematical expression}-dense extension of S. The complete meet-subsem...

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Publication status:
Published

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Publisher copy:
10.1007/s11083-013-9296-2

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Journal:
ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS
Volume:
31
Issue:
2
Pages:
189-216
Publication date:
2014-07-01
DOI:
EISSN:
1572-9273
ISSN:
0167-8094
Source identifiers:
388044
Keywords:
Pubs id:
pubs:388044
UUID:
uuid:980d1d23-36c7-4d6e-aba2-5a36e8286a9f
Local pid:
pubs:388044
Deposit date:
2013-11-17

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