Applications of Pcf Theory to the Study of Ideals On

Journal of Symbolic Logic 87 (3):967-994 (2022)
  Copy   BIBTEX

Abstract

Let$\kappa $be a regular uncountable cardinal, anda cardinal greater than or equal to$\kappa $. Revisiting a celebrated result of Shelah, we show that ifis close to$\kappa $and(= the least size of a cofinal subset of) is greater than, thencan be represented (in the sense of pcf theory) as a pseudopower. This can be used to obtain optimal results concerning the splitting problem. For example we show that ifand, then no$\kappa $-complete ideal onis weakly-saturated.

Categories

Keywords

Reprint years

DOI

10.1017/jsl.2022.4

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,349

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

My notes

Similar books and articles

Some Innovative Types of Fuzzy Ideals in AG-Groupoids.Faiz Muhammad Khan, Hidayat Ullah Khan, Safyan Mukhtar, Asghar Khan & Nor Haniza Sarmin - 2019 - Journal of Intelligent Systems 28 (4):649-667.
Analytic ideals and their applications.Sławomir Solecki - 1999 - Annals of Pure and Applied Logic 99 (1-3):51-72.
Q-pointness, P-pointness And Feebleness Of Ideals.Pierre Matet & Janusz Pawlikowski - 2003 - Journal of Symbolic Logic 68 (1):235-261.
Q-pointness, p-pointness and feebleness of ideals.Pierre Matet & Janusz Pawlikowski - 2003 - Journal of Symbolic Logic 68 (1):235-261.
Katětov order on Borel ideals.Michael Hrušák - 2017 - Archive for Mathematical Logic 56 (7-8):831-847.
The Concept of Ideals in Legal Theory.Sanne Taekema - 2003 - Kluwer Law International.
Yoshihiro Abe. Weakly normal filters and the closed unbounded filter on P k λ_. Proceedings of the American Mathematical Society, vol. 104 (1998), pp. 1226–1234. - Yoshihiro Abe. _Weakly normal filters and large cardinals_. Tsukuba journal of mathematics, vol. 16 (1992), pp. 487–494. - Yoshihiro Abe. _Weakly normal ideals on P k λ and the singular cardinal hypothesis_. Fundamenta mathematicae, vol. 143 (1993), pp. 97–106. - Yoshihiro Abe. _Saturation of fundamental ideals on P k λ_. Journal of the Mathematical Society of Japan, vol. 48 (1996), pp. 511–524. - Yoshihiro Abe. _Strongly normal ideals on P k λ and the Sup-function_. opology and its applications, vol. 74 (1996), pp. 97–107. - Yoshihiro Abe. _Combinatorics for small ideals on P k λ_. Mathematical logic quarterly, vol. 43 (1997), pp. 541–549. - Yoshihiro Abe and Masahiro Shioya. _Regularity of ultrafilters and fixed points of elementary embeddings. Tsukuba journal of mathematics, vol. 22 (1998), pp. 31–37. [REVIEW]Pierre Matet - 2002 - Bulletin of Symbolic Logic 8 (2):309-311.
Products of Ideals in MV -algebras.P. L. Belluce, A. Lettieri & S. Sessa - 2001 - Journal of Applied Non-Classical Logics 11 (3-4):341-350.
Weakly Normal Filters and the Closed Unbounded Filter on P κ λ Weakly Normal Filters and Large CardinalsWeakly Normal Ideals on  κ λ and the Singular Cardinal HypothesisSaturation of Fundamental Ideals on  κ λ Strongly Normal Ideals on  κ λ and the Sup-FunctionCombinatorics for Small Ideals on  κ λ Regularity of Ultrafilters and Fixed Points of Elementary Embeddings.Pierre Matet, Yoshihiro Abe & Masahiro Shioya - 2002 - Bulletin of Symbolic Logic 8 (2):309.
Ideals and Meaningfulness.Andr Grahle - 2000 - Rowman & Littlefield Publishers.
Combinatorics and forcing with distributive ideals.Pierre Matet - 1997 - Annals of Pure and Applied Logic 86 (2):137-201.
On Ideals Related to I[λ].Todd Eisworth - 2005 - Notre Dame Journal of Formal Logic 46 (3):301-307.
Game ideals.Pierre Matet - 2009 - Annals of Pure and Applied Logic 158 (1-2):23-39.
Donna M. Carr and Donald H. Pelletier. Towards a structure theory for ideals on Pkλ. Set theory and its applications, Proceedings of a conference held at York University, Ontario, Canada, Aug. 10–21, 1987, edited by J. Steprāns and S. Watson, Lecture notes in mathematics, vol. 1401, Springer-Verlag, Berlin etc. 1989, pp. 41–54. - William S. Zwicker. A beginning for structural properties of ideals on Pkλ. Set theory and its applications, Proceedings of a conference held at York University, Ontario, Canada, Aug. 10–21, 1987, edited by J. Steprāns and S. Watson, Lecture notes in mathematics, vol. 1401, Springer-Verlag, Berlin etc. 1989, pp. 201–217. [REVIEW]Alan D. Taylor - 1991 - Journal of Symbolic Logic 56 (3):1100-1101.
Descriptive set theory of families of small sets.Étienne Matheron & Miroslav Zelený - 2007 - Bulletin of Symbolic Logic 13 (4):482-537.

Analytics

Added to PP
2022-04-08

Downloads
21 (#715,461)

6 months
15 (#159,278)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

The secret life of μ-clubs.Pierre Matet - 2022 - Annals of Pure and Applied Logic 173 (9):103162.

Add more citations

References found in this work

On strong compactness and supercompactness.Telis K. Menas - 1975 - Annals of Mathematical Logic 7 (4):327-359.
Scales with various kinds of good points.Pierre Matet - 2018 - Mathematical Logic Quarterly 64 (4-5):349-370.
Weak saturation of ideals on Pκ(λ).Pierre Matet - 2011 - Mathematical Logic Quarterly 57 (2):149-165.
Two‐cardinal diamond star.Pierre Matet - 2014 - Mathematical Logic Quarterly 60 (4-5):246-265.

View all 11 references / Add more references