## 23 Citations

ZF+DC+AX_4

- Mathematics, Philosophy
- 2014

We consider mainly the following version of set theory: "ZF + DC and for every lambda, lambda^{aleph_0} is well ordered", our thesis is that this is a reasonable set theory, e.g. on the one hand it…

ZF + DC + AX4

- MathematicsArch. Math. Log.
- 2016

It is proved that for a sequence δ¯=⟨δs: s∈Y⟩,cf(δ s) large enough compared to Y, the pcf theorem can be proved with minor changes (in particular, using true cofinalities not the pseudo ones).

Reflexive Abelian Groups and Measurable Cardinals and Full Mad Families Sh904

- Mathematics

Answering problem (DG) of [1], [2], we show that there is a reflexive group of cardinality which equals to the first measurable cardinal. Anotated Contents §0 Introduction §1 A reflexive group above…

Pcf and abelian groups

- Mathematics
- 2007

Abstract. We deal with some pcf (possible cofinality theory) investigations mostly motivated by questions in abelian group theory. We concentrate on applications to test problems but we expect the…

SHELAH’S REVISED GCH AND A QUESTION BY ALON

- Mathematics
- 2011

The list-chromatic number χ`(G) of a graph G = (V,E) is the least cardinal κ such that for every assignment of a list L(V ) of at least κ colors to each vertex v ∈ V there is a proper vertex coloring…

PCF AND ABELIAN GROUPS SH898

- Mathematics
- 2013

We deal with some pcf (possible cofinality theory) investigations mostly motivated by questions in abelian group theory. We concentrate on ap- plications to test problems but we expect the…

Universality among graphs omitting a complete bipartite graph

- MathematicsComb.
- 2012

Under various assumptions mostly related to cardinal arithmetic the authors prove non-existence of universals for this problem of graphs of cardinality λ which has no subgraph which is (κ,θ)-complete bipartite graph.

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.

A note on the Revised GCH

- Mathematics
- 2021

We give a proof Theorem 2.10 from [8] that eliminates the use of Shelah’s nice filters and associated rank functions, and instead uses only the well-foundedness of reduced products of ordinals modulo…

PCF arithmetic without and with choice

- Mathematics
- 2009

We deal with relatives of GCH which are provable. In particular, we deal with rank version of the revised GCH. Our motivation was to find such results when only weak versions of the axiom of choice…

## References

SHOWING 1-10 OF 35 REFERENCES

The generalized continuum hypothesis revisited

- Mathematics
- 1998

We can reformulate the generalized continuum problem as: for regular κ<λ we have λ to the power κ is λ, We argue that the reasonable reformulation of the generalized continuum hypothesis, considering…

Reflecting stationary sets and successors of singular cardinals

- MathematicsArch. Math. Log.
- 1991

It is shown that supercompactness (and even the failure of PT) implies the existence of non-reflecting stationary sets, and that under suitable assumptions it is consistent that REF and there is a κ which is κ+n-supercompact.

Combinatorial problems on trees: Partitions, δ-systems and large free subtrees

- MathematicsAnn. Pure Appl. Log.
- 1987

Advances in Cardinal Arithmetic

- Mathematics
- 1993

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…

SUCCESSOR OF SINGULARS: COMBINATORICS AND NOT COLLAPSING CARDINALS ≤ κ IN (< κ)-SUPPORT ITERATIONS SH667

- Mathematics
- 2003

On the one hand we deal with (< κ)-supported iterated forcing notions which are (E0, E1)-complete, have in mind problems on Whitehead groups, uniformizations and the general problem. We deal mainly…

On squares, outside guessing of clubs and I_{

- Mathematics
- 1995

Suppose that lambda = mu^+. We consider two aspects of the square property on subsets of lambda. First, we have results which show e.g. that for aleph_0 <= kappa =cf (kappa)< mu, the equality…

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…

A consistency result on weak reflection

- Mathematics
- 1995

In this paper we study the notion of strong non-reflection, and its contrapositive weak reflection. We say theta strongly non-reflects at lambda iff there is a function F: theta ---> lambda such that…

Diamonds, uniformization

- MathematicsJournal of Symbolic Logic
- 1984

Abstract Assume G.C.H. We prove that for singular λ, □λ implies the diamonds hold for many S ⊆ λ+ (including S ⊆ {δ:δ ∈ λ+, cf δ = cf λ}.) We also have complementary consistency results.