Clones from Creatures
| dc.creator | Goldstern, Martin | |
| dc.creator | Shelah, Saharon | |
| dc.date | 2002-12-30 | |
| dc.date | 2003-02-24 | |
| dc.date.accessioned | 2026-07-07T04:54:08Z | |
| dc.date.available | 2026-07-07T04:54:08Z | |
| dc.description | A clone on a set X is a set of finitary operations on X which contains all the projections and is closed under composition. The set of all clones forms a complete lattice Cl(X) with greatest element O, the set of all finitary operations. For finite sets X the lattice is "dually atomic": every clone other than O is below a coatom of Cl(X). It was open whether Cl(X) is also dually atomic for infinite X. Assuming the continuum hypothesis, we show that there is a clone C on a countable set such that the interval of clones above C is linearly ordered, uncountable, and has no coatoms. | |
| dc.description | LaTeX2e, 20 pages. Revised version: some concepts simplified, proof details added | |
| dc.identifier | https://arxiv.org/abs/math/0212379 | |
| dc.identifier | http://arxiv.org/abs/math/0212379 | |
| dc.identifier | Trans. Amer. Math. Soc. 357 No. 9 (2005) 3525--3551 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/66125 | |
| dc.subject | Rings and Algebras | |
| dc.subject | Logic | |
| dc.subject | 08A40; 03E50 | |
| dc.title | Clones from Creatures | |
| dc.type | text |