Ultrafilters with property (s)
| dc.creator | Miller, Arnold W. | |
| dc.date | 2003-10-28 | |
| dc.date.accessioned | 2026-07-07T05:02:18Z | |
| dc.date.available | 2026-07-07T05:02:18Z | |
| dc.description | A set X which is a subset of the Cantor set has property (s) (Marczewski (Spzilrajn)) iff for every perfect set P there exists a perfect set Q contained in P such that Q is a subset of X or Q is disjoint from X. Suppose U is a nonprincipal ultrafilter on omega. It is not difficult to see that if U is preserved by Sacks forcing, i.e., it generates an ultrafilter in the generic extension after forcing with the partial order of perfect sets, then U has property (s) in the ground model. It is known that selective ultrafilters or even P-points are preserved by Sacks forcing. On the other hand (answering a question raised by Hrusak) we show that assuming CH (or more generally MA for ctble posets) there exists an ultrafilter U with property (s) such that U does not generate an ultrafilter in any extension which adds a new subset of omega. http://www.math.wisc.edu/~miller/res/index.html miller@math.wisc.edu | |
| dc.description | LaTeX2e 10 pages | |
| dc.identifier | https://arxiv.org/abs/math/0310438 | |
| dc.identifier | http://arxiv.org/abs/math/0310438 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69002 | |
| dc.subject | Logic | |
| dc.subject | 03E35; 03E17; 03E50 | |
| dc.title | Ultrafilters with property (s) | |
| dc.type | text |