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1
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The covering number for category and partition relations on $P_{ω}(λ)$

100%
Matet P.
Fundamenta Mathematicae
|
2002
|
tom 171
|
nr 3
235-247
EN
We show that cov(M) is the least infinite cardinal λ such that $P_ω(λ)$ (the set of all finite subsets of λ ) fails to satisfy a certain natural generalization of Ramsey's Theorem.
2
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Normal restrictions of the noncofinal ideal on $P_{κ}(λ)$

100%
Matet P.
Fundamenta Mathematicae
|
2013
|
tom 221
|
nr 1
1-22
EN
We discuss the problem of whether there exists a restriction of the noncofinal ideal on $P_κ(λ)$ that is normal.
3
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Large cardinals and covering numbers

100%
Matet P.
Fundamenta Mathematicae
|
2009
|
tom 205
|
nr 1
45-75
EN
The paper is concerned with the computation of covering numbers in the presence of large cardinals. In particular, we revisit Solovay's result that the Singular Cardinal Hypothesis holds above a strongly compact cardinal.
4
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Fragments of strong compactness, families of partitions and ideal extensions

64%
Fontanella L., Matet P.
Fundamenta Mathematicae
|
2016
|
tom 234
|
nr 2
171-190
EN
We investigate some natural combinatorial principles related to the notion of mild ineffability, and use them to obtain new characterizations of mild ineffable and weakly compact cardinals. We also show that one of these principles may be satisfied by a successor cardinal. Finally, we establish a version for $𝓟_{κ}(λ)$ of the canonical Ramsey theorem for pairs.
5
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On diamond sequences

32%
Matet P.
Fundamenta Mathematicae
|
1988
|
tom 131
|
nr 1
35-44
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