Nonreflecting stationary subsets of P κ λ

Yoshihiro Abe

Fundamenta Mathematicae (2000)

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

Abstract

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We explore the possibility of forcing nonreflecting stationary sets of P κ λ . We also present a P κ λ generalization of Kanamori’s weakly normal filters, which induces stationary reflection.

How to cite

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Abe, 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

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

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