Notre Dame Journal of Formal Logic

On Ideals Related to I[λ]

Todd Eisworth

Abstract

We describe a recipe for generating normal ideals on successors of singular cardinals. We show that these ideals are related to many weakenings of □ that have appeared in the literature. Our main purpose, however, is to provide an organized list of open questions related to these ideals.

Article information

Source
Notre Dame J. Formal Logic, Volume 46, Number 3 (2005), 301-307.

Dates
First available in Project Euclid: 30 August 2005

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1125409328

Digital Object Identifier
doi:10.1305/ndjfl/1125409328

Mathematical Reviews number (MathSciNet)
MR2160659

Zentralblatt MATH identifier
1092.03021

Subjects
Primary: 03E05: Other combinatorial set theory
Secondary: 03E65: Other hypotheses and axioms

Keywords
square combinatorial set theory ideals weak squares

Citation

Eisworth, Todd. On Ideals Related to I [λ]. Notre Dame J. Formal Logic 46 (2005), no. 3, 301--307. doi:10.1305/ndjfl/1125409328. https://projecteuclid.org/euclid.ndjfl/1125409328


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References

  • [1] Cummings, J., "Notes on singular cardinal combinatorics", Notre Dame Journal of Formal Logic, vol. 46 (2005), pp. 251--82.
  • [2] Eisworth, T., "Successors of singular cardinals", forthcoming chapter in the Handbook of Set Theory.
  • [3] Foreman, M., and M. Magidor, "A very weak square principle", The Journal of Symbolic Logic, vol. 62 (1997), pp. 175--96.
  • [4] Kojman, M., "The ABC of PCF", unpublished manuscript.
  • [5] Shelah, S., "Note on $I[\lambda]$", email correspondence.
  • [6] Shelah, S., "On successors of singular cardinals", pp. 357--80 in Logic Colloquium '78, vol. 97 of Studies in Logic and the Foundations of Mathematics, North-Holland, Amsterdam, 1979.