## On reflection of stationary sets in $\mathcal {P}_\kappa \lambda$

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- by Thomas Jech and Saharon Shelah PDF
- Trans. Amer. Math. Soc.
**352**(2000), 2507-2515 Request permission

## Abstract:

Let $\kappa$ be an inaccessible cardinal, and let $E_{0} = \{x \in \mathcal {P}_{\kappa }\kappa ^{+} : \text {cf} \; \lambda _{x} = \text {cf} \; \kappa _{x}\}$ and $E_{1} = \{x \in \mathcal {P}_{\kappa }\kappa ^{+} : \kappa _{x}$ is regular and $\lambda _{x} = \kappa _{x}^{+}\}$. It is consistent that the set $E_{1}$ is stationary and that every stationary subset of $E_{0}$ reflects at almost every $a \in E_{1}$.## References

- Hans-Dieter Donder, Peter Koepke, and Jean-Pierre Levinski,
*Some stationary subsets of ${\scr P}(\lambda )$*, Proc. Amer. Math. Soc.**102**(1988), no. 4, 1000–1004. MR**934882**, DOI 10.1090/S0002-9939-1988-0934882-6 - M. Foreman, M. Magidor, and S. Shelah,
*Martin’s maximum, saturated ideals, and nonregular ultrafilters. I*, Ann. of Math. (2)**127**(1988), no. 1, 1–47. MR**924672**, DOI 10.2307/1971415 - Thomas J. Jech,
*Some combinatorial problems concerning uncountable cardinals*, Ann. Math. Logic**5**(1972/73), 165–198. MR**325397**, DOI 10.1016/0003-4843(73)90014-4 - Thomas Jech and Saharon Shelah,
*Full reflection of stationary sets below $\aleph _\omega$*, J. Symbolic Logic**55**(1990), no. 2, 822–830. MR**1056391**, DOI 10.2307/2274667 - David W. Kueker,
*Countable approximations and Löwenheim-Skolem theorems*, Ann. Math. Logic**11**(1977), no. 1, 57–103. MR**457191**, DOI 10.1016/0003-4843(77)90010-9 - Richard Laver,
*Making the supercompactness of $\kappa$ indestructible under $\kappa$-directed closed forcing*, Israel J. Math.**29**(1978), no. 4, 385–388. MR**472529**, DOI 10.1007/BF02761175 - Menachem Magidor,
*Reflecting stationary sets*, J. Symbolic Logic**47**(1982), no. 4, 755–771 (1983). MR**683153**, DOI 10.2307/2273097 - S. Shelah,
*Strong partition relations below the power set: consistency; was Sierpiński right? II*, Sets, graphs and numbers (Budapest, 1991) Colloq. Math. Soc. János Bolyai, vol. 60, North-Holland, Amsterdam, 1992, pp. 637–668. MR**1218224** - S. Shelah,
*Iteration of $\lambda$-complete forcing not collapsing $\lambda ^{+}$*, [Sh 655] to appear.

## Additional Information

**Thomas Jech**- Affiliation: Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania 16802
- Email: jech@math.psu.edu
**Saharon Shelah**- Affiliation: Institute of Mathematics, The Hebrew University, Jerusalem, Israel
- MR Author ID: 160185
- ORCID: 0000-0003-0462-3152
- Received by editor(s): January 26, 1998
- Published electronically: April 20, 1999
- Additional Notes: Supported by NSF grants DMS-9401275 and DMS 97-04477
- © Copyright 2000 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**352**(2000), 2507-2515 - MSC (1991): Primary 03E35, 03E55
- DOI: https://doi.org/10.1090/S0002-9947-99-02448-4
- MathSciNet review: 1650097