Abstract
We construct a model in which for all 1 ≤ n < ω, there is no stationary subset of \({\aleph_{n+1} \cap {\rm cof}(\aleph_n)}\)which carries a partial square.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Cummings J.: Notes on singular cardinal combinatorics. Notre Dame J. Formal Log. 46(3), 251–282 (2005)
Cummings J., Wylie D.: More on full reflection below \({\aleph_\omega}\). Arch. Math. Log. 49(6), 659–671 (2010)
Krueger J., Schimmerling E.: An equiconsistency result on partial squares. J. Math. Log. 11(1), 1–31 (2011)
Magidor M.: Reflecting stationary sets. J. Symb. Log. 47(4), 755–771 (1982)
Sakai H.: Partial square at ω 1 is implied by MM but not by PFA. Fund. Math. 215, 109–131 (2011)
Shelah S.: Reflecting stationary sets and successors of singular cardinals. Arch. Math. Log. 31(1), 25–53 (1991)
Veličković B.: Jensen’s □ principles and the Novák number of partially ordered sets. J. Symb. Log. 51(1), 47–58 (1986)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Krueger, J. Successive cardinals with no partial square. Arch. Math. Logic 53, 11–21 (2014). https://doi.org/10.1007/s00153-013-0352-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00153-013-0352-9