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The weak □* is really weaker than the full □

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

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.

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[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.

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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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