| Title:
|
Forcing with ideals generated by closed sets (English) |
| Author:
|
Zapletal, Jindřich |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
43 |
| Issue:
|
1 |
| Year:
|
2002 |
| Pages:
|
181-188 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Consider the poset $P_I=\text{\rm Borel}(\Bbb R)\setminus I$ where $I$ is an arbitrary $\sigma$-ideal $\sigma$-generated by a projective collection of closed sets. Then the $P_I$ extension is given by a single real $r$ of an almost minimal degree: every real $s\in V[r]$ is Cohen-generic over $V$ or $V[s]=V[r]$. (English) |
| Keyword:
|
forcing |
| Keyword:
|
descriptive set theory |
| Keyword:
|
large cardinals |
| MSC:
|
03E15 |
| MSC:
|
03E17 |
| MSC:
|
03E40 |
| MSC:
|
03E55 |
| MSC:
|
03E60 |
| idZBL:
|
Zbl 1069.03037 |
| idMR:
|
MR1903318 |
| . |
| Date available:
|
2009-01-08T19:20:58Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119311 |
| . |
| Reference:
|
[B] Bartoszynski T., Judah H.: Set Theory: On the Structure of the Real Line.(1995), A K Peters Wellesley, Massachusetts. Zbl 0834.04001, MR 1350295 |
| Reference:
|
[J] Jech T.: Set Theory.(1978), Academic Press New York. Zbl 0419.03028, MR 0506523 |
| Reference:
|
[M] Martin D.A., Steel J.: A proof of projective determinacy.J. Amer. Math. Soc. (1989), 85 6582-6586. Zbl 0668.03021, MR 0959109 |
| Reference:
|
[N] Neeman I., Zapletal J.: Proper forcings and absoluteness in $L(\Bbb R)$.Comment. Math. Univ. Carolinae (1998), 39 281-301. Zbl 0939.03054, MR 1651950 |
| Reference:
|
[S] Solecki S.: Covering analytic sets by families of closed sets.J. Symbolic Logic 59 (1994), 1022-1031. Zbl 0808.03031, MR 1295987 |
| Reference:
|
[W] Woodin W.H.: Supercompact cardinals, sets of reals and weakly homogeneous trees.Proc. Natl. Acad. Sci. USA 85 6587-6591 (1988). Zbl 0656.03037, MR 0959110 |
| Reference:
|
[Z1] Zapletal J.: Isolating cardinal invariants.J. Math. Logic accepted. Zbl 1025.03046 |
| Reference:
|
[Z2] Zapletal J.: Countable support iteration revisited.J. Math. Logic submitted. |
| . |
