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STATIONARY REFLECTION

Part of: Set theory

Published online by Cambridge University Press:  08 January 2021

YAIR HAYUT  and
SPENCER UNGER
YAIR HAYUT
Affiliation:
DEPARTMENT FOR HAYUT IS EINSTEIN INSTITUTE OF MATHEMATICS EDMOND J. SAFRA CAMPUS THE HEBREW UNIVERSITY OF JERUSALEM GIVAT RAM, JERUSALEM9190401, ISRAELE-mail: [email protected]
SPENCER UNGER
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY OF TORONTOTORONTO, ONM5S 2E4, CANADAE-mail: [email protected]
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Abstract

We improve the upper bound for the consistency strength of stationary reflection at successors of singular cardinals.

Keywords

stationary reflectionsingular cardinalssubcompactPrikry forcingsquare

MSC classification

Primary: 03E35: Consistency and independence results
Secondary: 03E55: Large cardinals
Type
Articles
Information
The Journal of Symbolic Logic , Volume 85 , Issue 3 , September 2020 , pp. 937 - 959
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Copyright
© 2021, Journal of Symbolic Logic

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References

REFERENCES

Baumgartner, J. E., A new class of order types . Annals of Mathematical Logic , vol. 9 (1976), no. 3, pp. 187–222.CrossRefGoogle Scholar
Bukovskỳ, L., Characterization of generic extensions of models of set theory . Fundamenta Mathematicae , vol. 1 (1973), no. 83, pp. 35–46.CrossRefGoogle Scholar
Bukovskỳ, L., Iterated ultrapower and Prikry’s forcing . Commentationes Mathematicae Universitatis Carolinae , vol. 18 (1977), no. 1, pp. 77–85 (eng).Google Scholar
Cummings, J., A model in which GCH holds at successors but fails at limits . Transactions of the American Mathematical Society , vol. 329 (1992), no. 1, pp. 1–39.CrossRefGoogle Scholar
Cummings, J., Compactness and incompactness phenomena in set theory , Logic Colloquium 01 , Lecture Notes in Logic, vol. 20, Association for Symbolic Logic, Providence, RI, 2005, pp. 139–150.CrossRefGoogle Scholar
Cummings, J., Foreman, M., and Magidor, M., Squares, scales and stationary reflection . Journal of Mathematical Logic , vol. 1 (2001), no. 1, pp. 35–98.CrossRefGoogle Scholar
Dehornoy, P., Iterated ultrapowers and Prikry forcing . Annals of Mathematical Logic , vol. 15 (1978), no. 2, pp. 109–160.CrossRefGoogle Scholar
Faubion, Z., Improving the Consistency Strength of Stationary Set Reflection at ℵ ω+1 , Doctoral dissertation, University of California, Irvine, 2012.Google Scholar
Gitik, M., Prikry-Type Forcings , Springer, Dordrecht, Netherlands, 2010, pp. 1351–1447.Google Scholar
Harrington, L. and Shelah, S., Some exact equiconsistency results in set theory . Notre Dame Journal of Formal Logic , vol. 26 (1985), no. 2, pp. 178–188.CrossRefGoogle Scholar
Hayut, Y. and Lambie-Hanson, C., Simultaneous stationary reflection and square sequences, 2016. Preprint available from arXiv:1603.05556.CrossRefGoogle Scholar
Ishiu, T. and Yoshinobu, Y., Directive trees and games on posets . Proceedings of the American Mathematical Society , vol. 130 (2002), no. 5, pp. 1477–1485.CrossRefGoogle Scholar
Jensen, R. and Steel, J., K without the measurable, this Journal, vol. 78 (2013), no. 3, pp. 708–734.Google Scholar
Magidor, M., Reflecting stationary sets, this Journal, vol. 47 (1982), no. 4, pp. 755–771.Google Scholar
Magidor, M. and Lambie-Hanson, C., On the strengths and weaknesses of weak squares . Appalachian Set Theory , vol. 2006–2012 (2012), pp. 301–330.Google Scholar
Magidor, M. and Shelah, S., When does almost free imply free? (For groups, transversals, etc.) . Journal of the American Mathematical Society , vol. 7 (1994), pp. 769–830.CrossRefGoogle Scholar
Neeman, I. and Steel, J., Equiconsistenies at subcompact cardinals, submitted.Google Scholar
Schimmerling, E., Stationary reflection in extender models . Fundamenta Mathematicae , vol. 187 (2005), no. 2, pp. 161–169. MR 2214877.CrossRefGoogle Scholar
Schimmerling, E. and Zeman, M., Square in core models . Bulletin of Symbolic Logic , vol. 7 (2001), no. 3, pp. 305–314.CrossRefGoogle Scholar
Shelah, S., On incompactness for chromatic number of graphs . Acta Mathematica Hungarica , vol. 139 (2013), no. 4, pp. 363–371.CrossRefGoogle Scholar
Todorčević, S., On a conjecture of R. Rado . Journal of the London Mathematical Society , vol. s2–27 (1983), no. 1, pp. 1–8.CrossRefGoogle Scholar
Zeman, M., Two upper bounds on consistency strength of $\neg {\square}_{{\mathrm{\aleph}}_{\omega }}$ and stationary set reflection at two successive ℵn . Notre Dame Journal of Formal Logic , vol. 58 (2017), no. 3, pp. 409–432.CrossRefGoogle Scholar