Skip to main content
×
Home
    • Aa
    • Aa

The weak □* is really weaker than the full □

  • Shai Ben-David (a1) and Menachem Magidor (a2)
Abstract
Abstract

We show that relative to the consistency of a supercompact cardinal does not imply . The model-theoretic transfer property ⟨ℵ1, ℵ0⟩ → ⟨ℵω + 1, ℵω⟩ does not imply , and it is consistent to have an ultrafilter on ℵω + 1 which is λ-indecomposible for all ω < λ < ℵω.

Copyright
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[BS 86] S. Ben-David and S. Shelah , Non-special Aronszajn trees on ℵω + 1, Israel Journal of Mathematics, vol. 53 (1986), pp. 9396.

[M 77] M. Magidor , On the singular cardinals problem. I, Israel Journal of Mathematics, vol. 28, pp. 131.

[P71] K. Prikry , On descendingly complete ultrafilters, Cambridge summer school in mathematical logic (1971), Lecture Notes in Mathematics, vol. 337, Springer-Verlag, Berlin, 1973, pp. 459488.

[SRK 78] R. Solovay , W. Reinhardt and A. Kanamori , Strong axioms of infinity and elementary embeddings, Annals of Mathematical Logic, vol. 13, pp. 73116.

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

Abstract views

Total abstract views: 55 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 29th June 2017. This data will be updated every 24 hours.