# Nonreflecting stationary subsets of ${P}_{\kappa}\lambda $

Fundamenta Mathematicae (2000)

- Volume: 165, Issue: 1, page 55-66
- ISSN: 0016-2736

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topAbe, Yoshihiro. "Nonreflecting stationary subsets of $P_κλ$." Fundamenta Mathematicae 165.1 (2000): 55-66. <http://eudml.org/doc/212460>.

@article{Abe2000,

abstract = {We explore the possibility of forcing nonreflecting stationary sets of $P_κλ$. We also present a $P_κλ$ generalization of Kanamori’s weakly normal filters, which induces stationary reflection.},

author = {Abe, Yoshihiro},

journal = {Fundamenta Mathematicae},

keywords = {reflection of stationary sets; weak normality; inaccessible cardinal; cardinal preserving forcing notion},

language = {eng},

number = {1},

pages = {55-66},

title = {Nonreflecting stationary subsets of $P_κλ$},

url = {http://eudml.org/doc/212460},

volume = {165},

year = {2000},

}

TY - JOUR

AU - Abe, Yoshihiro

TI - Nonreflecting stationary subsets of $P_κλ$

JO - Fundamenta Mathematicae

PY - 2000

VL - 165

IS - 1

SP - 55

EP - 66

AB - We explore the possibility of forcing nonreflecting stationary sets of $P_κλ$. We also present a $P_κλ$ generalization of Kanamori’s weakly normal filters, which induces stationary reflection.

LA - eng

KW - reflection of stationary sets; weak normality; inaccessible cardinal; cardinal preserving forcing notion

UR - http://eudml.org/doc/212460

ER -

## References

top- [1] Y. Abe, Strongly normal ideals on ${P}_{\kappa}\lambda $ and the Sup-function, Topology Appl. 74 (1996), 97-107.
- [2] Y. Abe, Combinatorial characterization of ${\Pi}_{1}^{1}$-indescribability in ${P}_{\kappa}\lambda $, Arch. Math. Logic 37 (1998), 261-272.
- [3] A. Apter and S. Shelah, Menas' result is best possible, Trans. Amer. Math. Soc. 349 (1997), 2007-2034. Zbl0876.03030
- [4] D. M.Carr, A note on the λ-Shelah property, Fund. Math. 128 (1987), 197-198. Zbl0647.03041
- [5] D. M.Carr, J. P. Levinski and D. H. Pelletier, On the existence of strongly normal ideals on ${P}_{\kappa}\lambda $, Arch. Math. Logic 30 (1990), 59-72. Zbl0711.03019
- [6] M. Gitik, Nonsplitting stationary subsets of ${P}_{\kappa}{\kappa}^{+}$, J. Symbolic Logic 50 (1985), 881-894. Zbl0601.03021
- [7] T. Jech, Some combinatorial problems concerning uncountable cardinals, Ann. Math. Logic 5 (1973), 165-198. Zbl0262.02062
- [8] C. A.Johnson, Some partition relations for ideals on ${P}_{\kappa}\lambda $, Acta Math. Hungar. 56 (1990), 269-282. Zbl0733.03039
- [9] A. Kanamori, Weakly normal filters and irregular ultrafilters, Trans. Amer. Math. Soc. 220 (1976), 393-399. Zbl0341.02058
- [10] P. Koszmider, Semimorasses and nonreflection at singular cardinals, Ann. Pure Appl. Logic 72 (1995), 1-23. Zbl0843.03025
- [11] P. Matet, Concerning stationary subsets of ${\left[\lambda \right]}^{<\kappa}$, in: Set Theory and its Applications, Lecture Notes in Math. 1401, Springer, 1989, 119-127.

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