EUDML

The relations M(κ,λ,μ) → B [resp. B(σ)] meaning that if $A \subset {[κ]}^{λ}$ with |A|=κ is μ-almost disjoint then A has property B [resp. has a σ-transversal] had been introduced and studied under GCH in [EH]. Our two main results here say the following: Assume GCH and let ϱ be any regular cardinal with a supercompact [resp. 2-huge] cardinal above ϱ. Then there is a ϱ-closed forcing P such that, in $V^{P}$ , we have both GCH and $M (ϱ^{(+ ϱ + 1)}, ϱ^{+}, ϱ) ↛ B$ [resp. $M (ϱ^{(+ ϱ + 1)}, λ, ϱ) ↛ B (ϱ^{+})$ for all $λ \leq ϱ^{(+ ϱ + 1)}]$ . These show that, consistently, the results of [EH] are sharp. The necessity...

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On Large Chromatic Graphs Not Containing Prescribed Subgraphs

Remarks on the theorem of W. P. Hanf

On some combinatorial problems involving large cardinals

Proof of a conjecture of B. Ruziewicz

Some remarks on set theory XI

On hereditarily α-Lindelöf and α-separable spaces, II

On a classification of denumerable order types and an application to the partition calculus

A proof (involving Martin's axiom) of a partition relation

On the Ramsey-Turán number of finite graphs

On Pixley-Roy hyperspaces

Strongly almost disjoint familes, revisited

On the topological product of discrete $λ$ -compact spaces

Edge decompositions of graphs with no large independent sets.

Problems