Partitions of Groups

Протасов, Ігор; Slobodianiuk, Sergii

doi:10.17654/aadmjan2015_033_060

Cited by 2 publications

(2 citation statements)

References 27 publications

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“…In fact, this statement can be essentially strengthened: there is a function f : N → N such that, for every n-partition P of a G-space X, there are A ∈ P and F ⊂ G such that G = F ∆(A) and |F | f (n). This is an old open problem (see the surveys [2,22] whether the above statement is true with…”

Section: Proof (I) We Suppose That a Is Large And Choosementioning

confidence: 99%

Ultrafilters on $G$-spaces

Petrenko,

Protasov

2015

Preprint

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For a discrete group G and a discrete G-space X, we identify the Stone-Čech compactifications βG and βX with the sets of all ultrafilters on G and X, and apply the natural action of βG on βX to characterize large, thick, thin, sparse and scattered subsets of X. We use Ginvariant partitions and colorings to define G-selective and G-Ramsey ultrafilters on X. We show that, in contrast to the set-theoretical case, these two classes of ultrafilters are distinct. We consider also universally thin ultrafilters on ω, the T -points, and study interrelations between these ultrafilters and some classical ultrafilters on ω.

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Section: Proof (I) We Suppose That a Is Large And Choosementioning

confidence: 99%

Ultrafilters on $G$-spaces

Petrenko,

Protasov

2015

Preprint

Self Cite

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show abstract

“…

We systematize and analyze some results obtained in Subset Combinatorics of G groups after publications the previous surveys [1][2][3][4]. The main topics: the dynamical and descriptive characterizations of subsets of a group relatively their combinatorial size, Ramsey-product subsets in connection with some general concept of recurrence in G-spaces, new ideals in the Boolean algebra P G of all subsets of a group G and in the Stone-Čech compactification βG of G , the combinatorial derivation.

…”

mentioning

confidence: 99%