Wyniki wyszukiwania - BazTech

Ograniczanie wyników

2 Reports on Mathematical Logic

Znaleziono wyników: 2

Liczba wyników na stronie

Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

Some results on polish groups

Paolini Gianluca, Shelah Saharon

Reports on Mathematical Logic

2020

Vol. 55

61--71

We prove that no quantifier-free formula in the language of group theory can define the ℵ1-half graph in a Polish group, thus generalising some results from [6]. We then pose some questions on the space of groups of automorphisms of a given Borel complete class, and observe that this space must contain at least one uncountable group. Finally, we prove some results on the structure of the group of automorphisms of a locally finite group: firstly, we prove that it is not the case that every group of automorphisms of a graph of power λ is the group of automorphism of a locally finite group of power λ; secondly, we conjecture that the group of automorphisms of a locally finite group of power λ has a locally finite subgroup of power λ, and reduce the problem to a problem on p-groups, thus settling the conjecture in the case λ = ℵ0.

Borel sets without perfectly many overlapping translations

Rosłanowski Andrzej, Shelah Saharon

Reports on Mathematical Logic

2019

Vol. 54

3--43

We study the existence of Borel sets B ⊆ ω2 admitting a sequence ηα : α<λ of distinct elements of ω2 such that (ηα +B)∩(ηβ +B) ≥ 6 for all α, β < λ but with no perfect set of such η’s. Our result implies that under the Martin Axiom, if ℵα < c, α<ω1 and 3 ≤ ι<ω, then there exists a Σ0 2 set B ⊆ ω2 which has ℵα many pairwise 2ι–nondisjoint translations but not a perfect set of such translations. Our arguments closely follow Shelah [7, Section 1].