AUC Philosophica et Historica je víceoborový akademický časopis zaměřený na humanitní a společenskovědné obory (filozofie, psychologie, pedagogika, sociologie, obecné, české a hospodářské dějiny, pomocné vědy historické a archivnictví, etnologie).
Časopis je indexován v databázích CEEOL, DOAJ a EBSCO.
AUC PHILOSOPHICA ET HISTORICA, Vol 2017 No 2 (2017), 63–72
Grigorieff forcing and the tree property
Šárka Stejskalová
DOI: https://doi.org/10.14712/24647055.2017.16
zveřejněno: 14. 11. 2017
Abstract
In this paper we use Grigorieff forcing to obtain the tree property at the second successor of a regular uncountable cardinal κ. We also show that Silver forcing can be used to obtain the tree property at ℵ2.
klíčová slova: Grigorieff forcing; Silver forcing; tree property
reference (13)
1. Brooke M. Adersen and Marcia J. Groszek. Grigorieff forcing on uncountable cardinals does not add a generic of minimal degree. Notre Dame Journal of Formal Logic, 50(12): 221–231, 2009.
2. James Baumgartner. Iterated forcing. In A.R.D. Mathias, editor, Surveys in Set Theory, London Mathematical Society Lecture Note Series 87, pages 1–59. Cambridge University Press, 1983. CrossRef
3. James Baumgartner and Richard Laver. Iterated perfect-set forcing. Annals of Mathematical Logic, 17: 271–288, 1979. CrossRef
4. James Cummings. Iterated forcing and elementary embeddings. In Matthew Foreman and Akihiro Kanamori, editors, Handbook of Set Theory, volume 2, pages 737–774. Springer, 2010. CrossRef
5. Sy-David Friedman and Radek Honzik. The tree property at the ℵ2n's and the failure of SCH at ℵω. Annals of Pure and Applied Logic, 166: 526–552, 2015. CrossRef
6. Serge Grigorieff. Combinatorics on ideals and forcing. Annals of Mathematical Logic, 3(4): 363–394, 1971. CrossRef
7. Radek Honzik and Jonathan Verner. A lifting argument for the generalized Grigorieff forcing. Notre Dame Journal of Formal Logic, 57(2): 221–231, 2016. CrossRef
8. Thomas Jech. Set Theory. Springer Monographs in Mathematics. Springer-Verlag, Berlin, 2003.
9. Ronald Jensen. The fine structure of the constructible hierarchy. Annals of Mathematical Logic, 4: 229–308, 1972. CrossRef
10. Akihiro Kanamori. Perfect-set forcing for uncountable cardinals. Annals of Mathematical Logic, 19: 97–114, 1980. CrossRef
11. William Mitchell. Aronszajn trees and independence of the transfer property. Annals of Mathematical Logic, 5: 21–46, 1972. CrossRef
12. Ernst Specker. Sur un problème de Sikorski. Colloquium Mathematicum, 2: 9–12, 1949. CrossRef
13. Spencer Unger. Fragility and indestructibility of the tree property. Archive for Mathematical Logic, 51(5–6): 635–645, 2012. CrossRef
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