Advances in Cardinal Arithmetic
@article{Shelah1993AdvancesIC,
title={Advances in Cardinal Arithmetic},
author={Saharon Shelah},
journal={arXiv: Logic},
year={1993},
pages={355-383}
}If cfκ = κ, κ + < cfλ = λ then there is a stationary subset S of {δ < λ : cf(δ) = κ} in I[λ]. Moreover, we can find C = 〈C δ : δ ∈ S〉, C δ club of λ, otp(C δ ) = κ, guessing clubs and for each α < λ we have: {C δ ⋂ α: α ∈ naccC δ } has cardinality < λ.
104 Citations
A PARTITION RELATION USING STRONGLY COMPACT CARDINALS SH761
- Philosophy
- 2011
If κ is strongly compact and λ > κ and λ is regular (or alternatively cf(λ) ≥ κ), then ( 2 )+ → (λ+ ζ) θ holds for ζ, θ < κ. 2000 Mathematics Subject Classification. 2000 Math Subject Classification:…
Further cardinal arithmetic
- Mathematics
- 1996
We continue the investigations in the author’s book on cardinal arithmetic, assuming some knowledge of it. We deal with the cofinality of (S≤ℵ0(κ), ⊆) for κ real valued measurable (Section 3),…
Middle diamond
- MathematicsArch. Math. Log.
- 2005
Abstract.Under certain cardinal arithmetic assumptions, we prove that for every large enough regular λ cardinal, for many regular κ < λ, many stationary subsets of λ concentrating on cofinality κ has…
Subsets of cf ( μ ) μ , Boolean Algebras and Maharam measure
- Mathematics
- 1998
The original theme of the paper is the existence proof of “there is η̄ = 〈ηα : α < λ〉 which is a (λ, J)-sequence for Ī = 〈Ii : i < δ〉, a sequence of ideals. This can be thought of as in a…
Mathematical Logic
- Philosophy, Mathematics
- 2004
§1 A forcing axiom for λ > א1 fails [The forcing axiom is: if P is a forcing notion preserving stationary subsets of any regular uncountable μ ≤ λ and i is dense open subset of P for i < λ then some…
A partition relation using strongly compact cardinals
- Mathematics
- 2001
If κ is strongly compact and A > κ and A is regular (or alternatively cf(A) > κ), then (2 <λ ) + → (λ + ζ) 2 θ holds for ζ, θ < κ.
Reflection Implies the Sch Sh794
- Mathematics
We prove that, e.g., if μ > cf(μ) = א0 and μ > 20 and every stationary family of countable subsets of μ reflect in some subset of μ of cardinality א1 then the SCH for μ holds (moreover, for μ, any…
Bounds for covering numbers
- MathematicsJournal of Symbolic Logic
- 2006
Under various assumptions about the sizes of covering families for cardinals below λ, it is proved upper bounds for the covering number COV (λ. ν+. 2) is closely related to the cofinality of the partial order.
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This paper deals with variety of problems in pcf theory and infinitary combinatorics, looking at normal filters and prc, measures of the size of [lambda]^{ with |B_i|<mu_i, and the existence of strongly almost disjoint families.
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