Hostname: page-component-797576ffbb-k7d4m Total loading time: 0 Render date: 2023-12-06T11:45:13.567Z Has data issue: false Feature Flags: { "corePageComponentGetUserInfoFromSharedSession": true, "coreDisableEcommerce": false, "useRatesEcommerce": true } hasContentIssue false

Full reflection of stationary sets below ℵω

Published online by Cambridge University Press:  12 March 2014

Thomas Jech
Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania 16802
Saharon Shelah
Institute of Mathematics, The Hebrew University, Jerusalem, Israel


It is consistent that, for every n ≥ 2, every stationary subset of ωn consisting of ordinals of cofinality ωκ, where κ = 0 or κn − 3, reflects fully in the set of ordinals of cofinality ωn−1. We also show that this result is best possible.

Research Article
Copyright © Association for Symbolic Logic 1990

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)



[1]Jech, T., Stationary subsets of inaccessible cardinals, Axiomatic set theory (Baumgartner, al., editors), Contemporary Mathematics, vol. 31, American Mathematical Society, Providence, Rhode Island, 1984, pp. 115142.Google Scholar
[2]Magidor, M., Reflecting stationary sets, this Journal, vol. 47 (1982), pp. 755771.Google Scholar
[3]Shelah, S. [Sh 247], More on stationary coding, Around classification theory of models, Lecture Notes in Mathematics, vol. 1182, Springer-Verlag, Berlin, 1986, pp. 224246.Google Scholar
[4]Shelah, S. [Sh 351], Reflecting stationary sets and successors of singular cardinals (to appear).Google Scholar