| Title:
|
Club-guessing, good points and diamond (English) |
| Author:
|
Matet, Pierre |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
48 |
| Issue:
|
2 |
| Year:
|
2007 |
| Pages:
|
211-216 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Shelah's club-guessing and good points are used to show that the two-cardinal diamond principle $\lozenge_{\kappa,\lambda}$ holds for various values of $\kappa$ and $\lambda$. (English) |
| Keyword:
|
$P_\kappa(\lambda)$ |
| Keyword:
|
diamond principle |
| MSC:
|
03E05 |
| idZBL:
|
Zbl 1199.03031 |
| idMR:
|
MR2338089 |
| . |
| Date available:
|
2009-05-05T17:02:21Z |
| Last updated:
|
2012-05-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119651 |
| . |
| Reference:
|
[1] Cummings J., Foreman M., Magidor M.: Canonical structure in the universe of set theory, part one.Ann. Pure Appl. Logic 129 (2004), 211-243. MR 2078366 |
| Reference:
|
[2] Donder H.-D., Matet P.: Two cardinal versions of diamond.Israel J. Math. 83 (1993), 1-43. Zbl 0798.03047, MR 1239715 |
| Reference:
|
[3] Foreman M., Magidor M.: Mutually stationary sequences of sets and the non-saturation of the non-stationary ideal on $\Cal P_\kappa(\lambda)$.Acta Math. 186 (2001), 271-300. MR 1846032 |
| Reference:
|
[4] Jech T.J.: Some combinatorial problems concerning uncountable cardinals.Ann. Math. Logic 5 (1973), 165-198. Zbl 0262.02062, MR 0325397 |
| Reference:
|
[5] Kojman M.: The $A, B, C$ of pcf: a companion to pcf theory, part I.1995, unpublished. |
| Reference:
|
[6] Matet P.: Concerning stationary subsets of $[\lambda]^{<\kappa}$.in: Set Theory and its Applications (J. Steprāns and S. Watson, eds.), Lecture Notes in Mathematics 1401, Springer, Berlin, 1989, pp.119-127. MR 1031769 |
| Reference:
|
[7] Matet P.: Game ideals.preprint. MR 2502486 |
| Reference:
|
[8] Shioya M.: Splitting $\Cal P_\kappa\lambda$ into maximally many stationary sets.Israel J. Math. 114 (1999), 347-357. Zbl 0955.03047, MR 1738689 |
| Reference:
|
[9] Solovay R.M.: Real-valued measurable cardinals.in: Axiomatic Set Theory (D.S. Scott, ed.), Proceedings of Symposia in Pure Mathematics, vol. 13, part 1, American Mathematical Society, Providence, 1971, pp.397-428. Zbl 0222.02078, MR 0290961 |
| . |
