Antichains in partially ordered sets of singular cofinality
| dc.creator | Rinot, Assaf | |
| dc.date | 2006-06-01 | |
| dc.date | 2006-12-17 | |
| dc.date.accessioned | 2026-07-07T07:35:31Z | |
| dc.date.available | 2026-07-07T07:35:31Z | |
| dc.description | In their paper from 1981, Milner and Sauer conjectured that for any poset P, if cf(P)=lambda>cf(lambda)=kappa, then P must contain an antichain of size kappa. We prove that for lambda>cf(lambda)=kappa, if there exists a cardinal mu<lambda such that cov(lambda,mu,kappa,2)=lambda, then any poset of cofinality lambda contains lambda^kappa antichains of size kappa. The hypothesis of our theorem is very weak and is a consequence of many well-known axioms such as GCH, SSH and PFA. The consistency of the negation of this hypothesis is unknown. | |
| dc.description | 8 pages, reorganized structure | |
| dc.identifier | https://arxiv.org/abs/math/0606021 | |
| dc.identifier | http://arxiv.org/abs/math/0606021 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/120118 | |
| dc.subject | Logic | |
| dc.subject | Combinatorics | |
| dc.subject | 03E04, 03E35, 06A07 | |
| dc.title | Antichains in partially ordered sets of singular cofinality | |
| dc.type | text |