1,199 research outputs found
Generic Automorphisms and Green Fields
We show that the generic automorphism is axiomatisable in the green field of
Poizat (once Morleyised) as well as in the bad fields which are obtained by
collapsing this green field to finite Morley rank. As a corollary, we obtain
"bad pseudofinite fields" in characteristic 0. In both cases, we give geometric
axioms. In fact, a general framework is presented allowing this kind of
axiomatisation. We deduce from various constructibility results for algebraic
varieties in characteristic 0 that the green and bad fields fall into this
framework. Finally, we give similar results for other theories obtained by
Hrushovski amalgamation, e.g. the free fusion of two strongly minimal theories
having the definable multiplicity property. We also close a gap in the
construction of the bad field, showing that the codes may be chosen to be
families of strongly minimal sets.Comment: Some minor changes; new: a result of the paper (Cor 4.8) closes a gap
in the construction of the bad fiel
On the Scope of the Universal-Algebraic Approach to Constraint Satisfaction
The universal-algebraic approach has proved a powerful tool in the study of
the complexity of CSPs. This approach has previously been applied to the study
of CSPs with finite or (infinite) omega-categorical templates, and relies on
two facts. The first is that in finite or omega-categorical structures A, a
relation is primitive positive definable if and only if it is preserved by the
polymorphisms of A. The second is that every finite or omega-categorical
structure is homomorphically equivalent to a core structure. In this paper, we
present generalizations of these facts to infinite structures that are not
necessarily omega-categorical. (This abstract has been severely curtailed by
the space constraints of arXiv -- please read the full abstract in the
article.) Finally, we present applications of our general results to the
description and analysis of the complexity of CSPs. In particular, we give
general hardness criteria based on the absence of polymorphisms that depend on
more than one argument, and we present a polymorphism-based description of
those CSPs that are first-order definable (and therefore can be solved in
polynomial time).Comment: Extended abstract appeared at 25th Symposium on Logic in Computer
Science (LICS 2010). This version will appear in the LMCS special issue
associated with LICS 201
Imaginaries in separably closed valued fields
We show that separably closed valued fields of finite imperfection degree
(either with lambda-functions or commuting Hasse derivations) eliminate
imaginaries in the geometric language. We then use this classification of
interpretable sets to study stably dominated types in those structures. We show
that separably closed valued fields of finite imperfection degree are
metastable and that the space of stably dominated types is strict
pro-definable
The domination monoid in henselian valued fields
We study the domination monoid in various classes of structures arising from
the model theory of henselian valuations, including RV-expansions of henselian
valued fields of residue characteristic 0 (and, more generally, of benign
valued fields), p-adically closed fields, monotone D-henselian differential
valued fields with many constants, regular ordered abelian groups, and pure
short exact sequences of abelian structures. We obtain Ax-Kochen-Ershov type
reductions to suitable fully embedded families of sorts in quite general
settings, and full computations in concrete ones.Comment: 35 pages. Minor revisio
Some definable types that cannot be amalgamated
We exhibit a theory where definable types lack the amalgamation property.Comment: 4 page
Beautiful pairs
We introduce an abstract framework to study certain classes of stably
embedded pairs of models of a complete -theory , called
beautiful pairs, which comprises Poizat's belles paires of stable structures
and van den Dries-Lewenberg's tame pairs of o-minimal structures. Using an
amalgamation construction, we relate several properties of beautiful pairs with
classical Fra\"{i}ss\'{e} properties.
After characterizing beautiful pairs of various theories of ordered abelian
groups and valued fields, including the theories of algebraically, -adically
and real closed valued fields, we show an Ax-Kochen-Ershov type result for
beautiful pairs of henselian valued fields. As an application, we derive strict
pro-definability of particular classes of definable types. When is one of
the theories of valued fields mentioned above, the corresponding classes of
types are related to classical geometric spaces such as Berkovich and Huber's
analytifications. In particular, we recover a result of Hrushovski-Loeser on
the strict pro-definability of stably dominated types in algebraically closed
valued fields.Comment: 40 page
Some Definability Results in Abstract Kummer Theory
Let be a semiabelian variety over an algebraically closed field, and let
be an irreducible subvariety not contained in a coset of a proper algebraic
subgroup of . We show that the number of irreducible components of
is bounded uniformly in , and moreover that the bound is
uniform in families .
We prove this by purely Galois-theoretic methods. This proof applies in the
more general context of divisible abelian groups of finite Morley rank. In this
latter context, we deduce a definability result under the assumption of the
Definable Multiplicity Property (DMP). We give sufficient conditions for finite
Morley rank groups to have the DMP, and hence give examples where our
definability result holds.Comment: 21 pages; minor notational fixe
Influence of patch size and chemistry on the catalytic activity of patchy hybrid nonwovens
In this work, we provide a detailed study on the influence of patch size and chemistry on the catalytic activity of patchy hybrid nonwovens in the gold nanoparticle (Au NP) catalysed alcoholysis of dimethylphenylsilane in n-butanol. The nonwovens were produced by coaxial electrospinning, employing a polystyrene solution as the core and a dispersion of spherical or worm-like patchy micelles with functional, amino group-bearing patches (dimethyl and diisopropyl amino groups as anchor groups for Au NP) as the shell. Subsequent loading by dipping into a dispersion of preformed Au NPs yields the patchy hybrid nonwovens. In terms of NP stabilization, i.e., preventing agglomeration, worm-like micelles with poly(N,N-dimethylaminoethyl methacrylamide) (PDMA) patches are most efficient. Kinetic studies employing an extended 1(st) order kinetics model, which includes the observed induction periods, revealed a strong dependence on the accessibility of the Au NPs' surface to the reactants. The accessibility is controlled by the swellability of the functional patches in n-butanol, which depends on both patch chemistry and size. As a result, significantly longer induction (t(ind)) and reaction (t(R)) times were observed for the 1(st) catalysis cycles in comparison to the 10(th) cycles and nonwovens with more polar PDMA patches show a significantly lower t(R) in the 1(st) catalysis cycle. Thus, the unique patchy surface structure allows tailoring the properties of this "tea-bag"-like catalyst system in terms of NP stabilization and catalytic performance, which resulted in a significant reduction of t(R) to about 4 h for an optimized system
- …