1,545 research outputs found
Connected components of definable groups and o-minimality I
We give examples of groups G such that G^00 is different from G^000. We also
prove that for groups G definable in an o-minimal structure, G has a "bounded
orbit" iff G is definably amenable. These results answer questions of
Gismatullin, Newelski, Petrykovski. The examples also give new non G-compact
first order theories.Comment: 26 pages. This paper corrects the paper "Groups definable in
o-minimal structures: structure theorem, G^000, definable amenability, and
bounded orbits" by the first author which was posted in December
(1012.4540v1) and later withdraw
Henselian valued fields and inp-minimality
We prove that every ultraproduct of -adics is inp-minimal (i.e., of burden
). More generally, we prove an Ax-Kochen type result on preservation of
inp-minimality for Henselian valued fields of equicharacteristic in the RV
language.Comment: v.2: 15 pages, minor corrections and presentation improvements;
accepted to the Journal of Symbolic Logi
Pseudofinite structures and simplicity
We explore a notion of pseudofinite dimension, introduced by Hrushovski and
Wagner, on an infinite ultraproduct of finite structures. Certain conditions on
pseudofinite dimension are identified that guarantee simplicity or
supersimplicity of the underlying theory, and that a drop in pseudofinite
dimension is equivalent to forking. Under a suitable assumption, a
measure-theoretic condition is shown to be equivalent to local stability. Many
examples are explored, including vector spaces over finite fields viewed as
2-sorted finite structures, and homocyclic groups. Connections are made to
products of sets in finite groups, in particular to word maps, and a
generalization of Tao's algebraic regularity lemma is noted
Model Theory: groups, geometry, and combinatorics
This conference was about recent interactions of model theory with combinatorics, geometric group theory and the theory of valued fields, and the underlying pure model-theoretic developments. Its aim was to report on recent results in the area, and to foster communication between the different communities
Colloid-polymer mixtures in the protein limit
We computed the phase-separation behavior and effective interactions of
colloid-polymer mixtures in the "protein limit", where the polymer radius of
gyration is much larger than the colloid radius. For ideal polymers, the
critical colloidal packing fraction tends to zero, whereas for interacting
polymers in a good solvent the behavior is governed by a universal binodal,
implying a constant critical colloid packing fraction. In both systems the
depletion interaction is not well described by effective pair potentials but
requires the incorporation of many-body contributions.Comment: 4 pages, 3 figures, submitted to Physical Review Letter
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