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SEPARATING DIAGONAL STATIONARY REFLECTION PRINCIPLES

Part of: Set theory

Published online by Cambridge University Press:  15 February 2021

GUNTER FUCHS  and
CHRIS LAMBIE-HANSON
GUNTER FUCHS
Affiliation:
THE COLLEGE OF STATEN ISLAND THE CITY UNIVERSITY OF NEW YORK 2800 VICTORY BLVD., STATEN ISLAND, NEW YORK, NY 10314, USA and THE GRADUATE CENTER THE CITY UNIVERSITY OF NEW YORK 365 5TH AVENUE, NEW YORK, NY 10016, USA E-mail: gunter.fuchs@csi.cuny.edu
CHRIS LAMBIE-HANSON
Affiliation:
DEPARTMENT OF MATHEMATICS AND APPLIED MATHEMATICS VIRGINIA COMMONWEALTH UNIVERSITYRICHMOND, VA23284, USAE-mail: cblambiehanso@vcu.edu
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Abstract

We introduce three families of diagonal reflection principles for matrices of stationary sets of ordinals. We analyze both their relationships among themselves and their relationships with other known principles of simultaneous stationary reflection, the strong reflection principle, and the existence of square sequences.

Keywords

reflection principlessquare sequences

MSC classification

Primary: 03E05: Other combinatorial set theory
Secondary: 03E35: Consistency and independence results 03E55: Large cardinals 03E57: Generic absoluteness and forcing axioms
Type
Article
Information
The Journal of Symbolic Logic , Volume 86 , Issue 1 , March 2021 , pp. 262 - 292
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Copyright
© The Association for Symbolic Logic 2021

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References

REFERENCES

Abraham, U., Proper forcing , Handbook of Set Theory (Foreman, M. and Kanamori, A., editors), Springer, Dordrecht, 2010, pp. 333–394.CrossRefGoogle Scholar
Abraham, U. and Shelah, S., Forcing closed unbounded sets , this J ournal , vol. 48 (1983), no. 3, pp. 643–657.Google Scholar
Cummings, J., Iterated forcing and elementary embeddings , Handbook of Set Theory (Foreman, M. and Kanamori, A., editors), Springer, Dordrecht, 2010, pp. 775–883.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
Eisworth, T., Successors of singular cardinals , Handbook of Set Theory (Foreman, M. and Kanamori, A., editors), Springer, Dordrecht, 2010, pp. 1229–1350.CrossRefGoogle Scholar
Foreman, M., Ideals and generic elementary embeddings , Handbook of Set Theory (Foreman, M. and Kanamori, A., editors), Springer, Dordrecht, 2010, pp. 885–1147.CrossRefGoogle Scholar
Fuchs, G., Diagonal reflections on squares . Archive for Mathematical Logic , vol. 58 (2019), no. 2, pp. 1–26.CrossRefGoogle Scholar
Hayut, Y. and Lambie-Hanson, C., Simultaneous stationary reflection and square sequences . Journal of Mathematical Logic , vol. 17 (2017), no. 2, p. 1750010, 27.CrossRefGoogle Scholar
Jech, T., Set Theory , Springer Monographs in Mathematics, Springer, Berlin and Heidelberg, 2003.Google Scholar
Kunen, K., Saturated ideals , this J ournal , vol. 43 (1978), no. 1, pp. 65–76.Google Scholar
Kurepa, D., Ensembles ordonnés et ramifiés de points . Mathematica Balkanica , vol. 7 (1977), pp. 201–204.Google Scholar
Lambie-Hanson, C., Squares and narrow systems , this J ournal , vol. 82 (2017), no. 3, pp. 834–859.Google Scholar
Lambie-Hanson, C. and Rinot, A., Knaster and friends II: The C-sequence number. Journal of Mathematical Logic , vol. 21 (2021), no. 1, 2150002.CrossRefGoogle Scholar
Larson, P., Separating stationary reflection principles , this J ournal , vol. 65 (2000), no. 1, pp. 247–258.Google Scholar
Larson, P., The Stationary Tower: Notes on a Course by W. Hugh Woodin , University Lecture Notes, 32, American Mathematical Society, Providence, RI, 2004.Google Scholar
Laver, R., Making the supercompactness of $\kappa$ indestructible under $\kappa$ -directed closed forcing . Israel Journal of Mathematics , vol. 29 (1978), no. 4, pp. 385–388.CrossRefGoogle Scholar
Magidor, M., Reflecting stationary sets , this J ournal , vol. 47 (1982), no. 4, pp. 755–771 (1983).Google Scholar
Woodin, W. H., The Axiom of Determinacy, Forcing Axioms and the Nonstationary Ideal , De Gruyter, Berlin and New York, 1999.CrossRefGoogle Scholar