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Amenability and Ramsey theory

100%

Moore J.

Fundamenta Mathematicae

2013

tom 220

nr 3

263-280

The purpose of this article is to connect the notion of the amenability of a discrete group with a new form of structural Ramsey theory. The Ramsey-theoretic reformulation of amenability constitutes a considerable weakening of the Følner criterion. As a by-product, it will be shown that in any non-amenable group G, there is a subset E of G such that no finitely additive probability measure on G measures all translates of E equally. The analysis of discrete groups will be generalized to the setting of automorphism groups of ultrahomogeneous structures.

Minimality of non-σ-scattered orders

63%

Ishiu T., Moore J.

Fundamenta Mathematicae

2009

tom 205

nr 1

29-44

We will characterize-under appropriate axiomatic assumptions-when a linear order is minimal with respect to not being a countable union of scattered suborders. We show that, assuming PFA⁺, the only linear orders which are minimal with respect to not being σ-scattered are either Countryman types or real types. We also outline a plausible approach to demonstrating the relative consistency of: There are no minimal non-σ-scattered linear orders. In the process of establishing these results, we will prove combinatorial characterizations of when a given linear order is σ-scattered and when it contains either a real or Aronszajn type.

Ograniczanie wyników

2 Fundamenta Mathematicae

2 Moore J.

1 Ishiu T.

1 2013

1 2009

Wyniki wyszukiwania

Amenability and Ramsey theory

Minimality of non-σ-scattered orders