Ramsey dichotomies with ordinal index
| dc.creator | Farmaki, V. | |
| dc.date | 1998-04-14 | |
| dc.date.accessioned | 2026-07-07T05:24:23Z | |
| dc.date.available | 2026-07-07T05:24:23Z | |
| dc.description | A system of uniform families on an infinite subset $M$ of $\nn$ is a collection $(\cca_ξ)_{ξ<ω_1}$ of families of finite subsets of $\nn$ (where, $\cca_k$ consists of all $k$--element subset of $M$, for $k\in \nn$) with the properties that each $\cca_ξ$ is thin (i.e. it does not contain proper initial segments of any of its element) and the Cantor--Bendixson index, defined for $\cca_ξ$, is equal to $ξ+1$ and stable when we restrict ourselves to any subset of $M$. We indicate how to extend the generalized Schreier families to a system of uniform families. Using that notion we establish the correct (countable) ordinal index generalization of the classical Ramsey theorem (which corresponds to the finite ordinal indices). | |
| dc.description | 26 pages | |
| dc.identifier | https://arxiv.org/abs/math/9804063 | |
| dc.identifier | http://arxiv.org/abs/math/9804063 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76820 | |
| dc.subject | Logic | |
| dc.subject | Functional Analysis | |
| dc.subject | 05D10, 46B45 | |
| dc.title | Ramsey dichotomies with ordinal index | |
| dc.type | text |