Partition properties of subsets of Pκλ
Shioya, Masahiro
Fundamenta Mathematicae, Tome 159 (1999), p. 325-329 / Harvested from The Polish Digital Mathematics Library

Let κ > ω be a regular cardinal and λ > κ a cardinal. The following partition property is shown to be consistent relative to a supercompact cardinal: For any f:n<ω[X]nγ with XPκλ unbounded and 1 < γ < κ there is an unbounded Y ∪ X with |f''[Y]n|=1 for any n < ω.

Publié le : 1999-01-01
EUDML-ID : urn:eudml:doc:212409
@article{bwmeta1.element.bwnjournal-article-fmv161i3p325bwm,
     author = {Masahiro Shioya},
     title = {Partition properties of subsets of P$\kappa$$\lambda$},
     journal = {Fundamenta Mathematicae},
     volume = {159},
     year = {1999},
     pages = {325-329},
     zbl = {0937.03056},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv161i3p325bwm}
}
Shioya, Masahiro. Partition properties of subsets of Pκλ. Fundamenta Mathematicae, Tome 159 (1999) pp. 325-329. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv161i3p325bwm/

[00000] [1] Y. Abe, Combinatorics for small ideals on Pκλ, Math. Logic Quart. 43 (1997), 541-549. | Zbl 0897.03049

[00001] [2] Y. Abe, private communication.

[00002] [3] J. Baumgartner, Iterated forcing, in: Surveys in Set Theory, A. Mathias (ed.), London Math. Soc. Lecture Note Ser. 87, Cambridge Univ. Press, Cambridge, 1983, 1-59.

[00003] [4] C. Di Prisco and W. Zwicker, Flipping properties and supercompact cardinals, Fund. Math. 109 (1980), 31-36. | Zbl 0464.03047

[00004] [5] R. Engelking and M. Karłowicz, Some theorems of set theory and their topological consequences, ibid. 57 (1965), 275-285. | Zbl 0137.41904

[00005] [6] T. Jech, Some combinatorial problems concerning uncountable cardinals, Ann. Math. Logic 5 (1973), 165-198. | Zbl 0262.02062

[00006] [7] T. Jech and S. Shelah, A partition theorem for pairs of finite sets, J. Amer. Math. Soc. 4 (1991), 647-656. | Zbl 0744.03048

[00007] [8] C. Johnson, Some partition relations for ideals on Pκλ, Acta Math. Hungar. 56 (1990), 269-282. | Zbl 0733.03039

[00008] [9] S. Kamo, Ineffability and partition property on Pκλ, J. Math. Soc. Japan 49 (1997), 125-143.

[00009] [10] A. Kanamori, The Higher Infinite, Springer, Berlin, 1994. | Zbl 0813.03034

[00010] [11] R. Laver, Making the supercompactness of κ indestructible under κ-directed closed forcing, Israel J. Math. 29 (1978), 385-388. | Zbl 0381.03039

[00011] [12] M. Magidor, Combinatorial characterization of supercompact cardinals, Proc. Amer. Math. Soc. 42 (1974), 279-285. | Zbl 0279.02050

[00012] [13] P. Matet, handwritten notes.

[00013] [14] T. Menas, A combinatorial property of Pκλ, J. Symbolic Logic 41 (1976), 225-234. | Zbl 0331.02045