## 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

#### 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

#### 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• [4] Kojman, M., "The ABC of PCF", unpublished manuscript.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.