Large intervals in the clone lattice
| dc.creator | Goldstern, Martin | |
| dc.creator | Shelah, Saharon | |
| dc.date | 2002-08-08 | |
| dc.date | 2004-07-29 | |
| dc.date.accessioned | 2026-07-07T04:50:08Z | |
| dc.date.available | 2026-07-07T04:50:08Z | |
| dc.description | We give three examples of large intervals in the lattice of (local) clones on an infinite set X, by exhibiting clones C_1, C_2, C_3 such that: (1) the interval [C_1, O] in the lattice of local clones is (as a lattice) isomorphic to {0,1,2, ...} under the divisibility relation, (2) the interval [C_2, O] in the lattice of local clones is isomorphic to the congruence lattice of an arbitrary semilattice, (3) the interval [C_3, O] in the lattice of all clones is isomorphic to the lattice of all filters on X. These examples explain the difficulty of obtaining a satisfactory analysis of the clone lattice on infinite sets. In particular, (1) shows that the lattice of local clones is not dually atomic. | |
| dc.description | LaTeX2e, 9 pages. Revised version contains additional comments and references | |
| dc.identifier | https://arxiv.org/abs/math/0208066 | |
| dc.identifier | http://arxiv.org/abs/math/0208066 | |
| dc.identifier | Algebra Universalis 62 No. 4 (2009) 367--374 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/64684 | |
| dc.subject | Rings and Algebras | |
| dc.subject | 08A40; 06A12, 08A05 | |
| dc.title | Large intervals in the clone lattice | |
| dc.type | text |