| Title:
|
Combinatorial trees in Priestley spaces (English) |
| Author:
|
Ball, Richard N. |
| Author:
|
Pultr, Aleš |
| Author:
|
Sichler, Jiří |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
46 |
| Issue:
|
2 |
| Year:
|
2005 |
| Pages:
|
217-234 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We show that prohibiting a combinatorial tree in the Priestley duals determines an axiomatizable class of distributive lattices. On the other hand, prohibiting $n$-crowns with $n\geq 3$ does not. Given what is known about the diamond, this is another strong indication that this fact characterizes combinatorial trees. We also discuss varieties of 2-Heyting algebras in this context. (English) |
| Keyword:
|
distributive lattice |
| Keyword:
|
Priestley duality |
| Keyword:
|
poset |
| Keyword:
|
first-order definable |
| MSC:
|
03C05 |
| MSC:
|
06A11 |
| MSC:
|
06D20 |
| MSC:
|
06D50 |
| MSC:
|
06D55 |
| MSC:
|
54F05 |
| idZBL:
|
Zbl 1121.06003 |
| idMR:
|
MR2176889 |
| . |
| Date available:
|
2009-05-05T16:50:44Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119521 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] Ball R.N., Pultr A.: Forbidden Forests in Priestley Spaces.Cahiers Topologie Géom. Différentielle Catég. 45 1 (2004), 2-22. Zbl 1062.06020, MR 2040660 |
| Reference:
|
[4] Ball R.N., Pultr A., Sichler J.: Priestley configurations and Heyting varieties.submitted for publication. Zbl 1165.06003 |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[9] Łoś J.: Quelques remarques, théorèmes et problèmes sur les classes définisables d'algèbres.Mathematical interpretation of formal systems, North-Holland, Amsterdam, 1955, pp.98-113. |
| Reference:
|
[10] Monteiro A.: L'arithmetique des filtres et les espaces topologiques.I, II, Notas de Lógica Matemática (1974), 29-30. Zbl 0318.06019 |
| Reference:
|
[11] Priestley H.A.: Representation of distributive lattices by means of ordered Stone spaces.Bull. London Math. Soc. 2 (1970), 186-190. Zbl 0201.01802, MR 0265242 |
| Reference:
|
[12] Priestley H.A.: Ordered topological spaces and the representation of distributive lattices.Proc. London Math. Soc. 324 (1972), 507-530. Zbl 0323.06011, MR 0300949 |
| . |
