Skip to main content
×
Home
    • Aa
    • Aa

Club guessing sequences and filters

  • Tetsuya Ishiu (a1)
Abstract
Abstract

We investigate club guessing sequences and filters. We prove that assuming V = L, there exists a strong club guessing sequence on μ if and only if μ is not ineffable for every uncountable regular cardinal μ. We also prove that for every uncountable regular cardinal μ, relative to the existence of a Woodin cardinal above μ, it is consistent that every tail club guessing ideal on μ is precipitous.

Copyright
References
Hide All
[1] James E. Baumgartner and Alan D. Taylor , Saturation properties of ideals in generic extensions, II, Transactions of the American Mathematical Society, vol. 271 (1982), no. 2, pp. 587609.

[3] Keith J. Devlin , Constructibility, Springer-Verlag, 1984.

[7] Matthew Foreman and Menachem Magidor , Large cardinals and definable counterexamples to the continuum hypothesis, Annals of Pure and Applied Logic, vol. 76 (1995), no. 1, pp. 4797.

[8] Matthew Foreman , Menachem Magidor , and Saharon Shelah , Martin's maximum, saturated ideals, and nonregular ultrafilters. I, Annals of Mathematics. 2nd Series, vol. 127 (1988), no. 1, pp. 147.

[9] Moti Gitik and Saharon Shelah , Less saturated ideals, Proceedings of the American Mathematical Society, vol. 125 (1997), no. 5, pp. 15231530.

[10] Noa Goldring , Woodin cardinals and presaturated ideals, Annals of Pure and Applied Logic, vol. 55 (1992), no. 3, pp. 285303.

[14] Thomas Jech and Karel Prikry , On ideals of sets and the power set operation, Bulletin of the American Mathematical Society, vol. 82 (1976), no. 4, pp. 593595.

[16] Ronald B. Jensen , The fine structure of the constructible hierarchy, Annals of Mathematical Logic, vol. 4 (1972), pp. 229308. with a section by Jack Silver.

[17] Akihiro Kanamori , The Higher Inifinite, Springer-Verlag, 1997.

[18] Menachem Kojman and Saharon Shelah , The universality spectrum of stable unsuperstable theories, Annals of Pure and Applied Logic, vol. 58 (1992), no. 1, pp. 5772.

[20] Andrzej Rosłanowski and Saharon Shelah , Iteration of λ-complete forcing notions not collapsing λ+, International Journal of Mathematics and Mathematical Sciences, vol. 28 (2001), pp. 6382.

[23] Saharon Shelah , Proper and Improper Forcing, 2nd ed., Perspectives in Mathematical Logic, Springer-Verlag, 1998.

[24] Robert M. Solovay , Real-valued Measurable Ccardinals, Axiomatic Set Theory ( D. Scott , editor), American Mathematical Society, 1971, pp. 397428.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 1 *
Loading metrics...

Abstract views

Total abstract views: 63 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 19th October 2017. This data will be updated every 24 hours.