7 citations · 35 across the 21 of their papers we have counts for
23 papers · 1 filter
Radon measures in the Berkovich space and generically stable measures in ACVF
Alf Onshuus, Mariana Vicaria
In this paper we study Keisler measures in models of ACVF. We give analogue definitions for a Keisler measure to be orthogonal to the value group and stably dominated using unique…
Limit Semigroups with 2 Generators
Felipe Estrada, Alf Onshuus, David Rincon
In this paper we study the limit theory of numerical semigroups with two generators. We give a complete axiomatization in some cases.
Strongly minimal group relics of algebraically closed valued fields
Alf Onshuus, Assaf Hasson, Santiago Pinzon
We prove Zilber's trichotomy for reducts of ACVF expanding or .
Continuous isomorphisms between groups definable in o-minimal expansions of the real field
Alf Onshuus
In this paper we study the relation between the category of real Lie groups and that of groups definable in o-minimal expansions of the real field, which we will refer to as ``defi…
Definably amenable groups in Continuous logic
Juan Felipe Carmona, Alf Onshuus
We introduce the notions of definable amenability and extreme definable amenability for groups in continuous structures and conduct an extensive analysis of them, drawing parallels…
Dependent finitely homogneneous rosy structures
Alf Onshuus, Pierre Simon
We study finitely homogeneous dependent rosy structures, adapting results of Cherlin, Harrington, and Lachlan proved for -stable -categorical structures. In particular, we pr…
Real Lie groups and o-minimality
Annalisa Conversano, Alf Onshuus, Sacha Post
We characterize, up to Lie isomorphism, the real Lie groups that are definable in an o-minimal expansion of the real field.
A definability criterion for connected Lie groups
Alf Onshuus, Sacha Post
It has been known since \cite{Pgroupchunk} that any group definable in an -minimal expansion of the real field can be equipped with a Lie group structure. It is therefore natura…
Uniform Continuity in Definable Groups
Alf Onshuus, Luis Carlos Suárez
In this paper we study analogues of amenability for topological groups in the context of definable structures. We prove fixed point theorems for such groups. More importantly, we p…
A fixed-point theorem for definably amenable groups
Juan Felipe Carmona, Kevin Dávila, Alf Onshuus +1
We prove an analogue of the fixed-point theorem for the case of definably amenable groups.
Definable groups in models of Presburger Arithmetic and G^{00}
Alf Onshuus, Mariana Vicaría
This paper is devoted to understand groups definable in Presburger arithmetic. We prove the following theorems: Theorem 1. Every group definable in a model of Presburger Arithmetic…
Stabilizers, groups with f-generics in NTP2 and PRC fields
Samaria Montenegro, Alf Onshuus, Pierre Simon
In this paper we develop three different subjects. We study and prove alternative versions of Hrushovski's "Stabilizer Theorem", we generalize part of the basic theory of definably…
Groups in NTP2
Nadja Hempel, Alf Onshuus
We prove the existence of abelian, solvable and nilpotent definable envelopes for groups definable in models of an NTP2 theory.
Solvable Lie groups definable in o-minimal theories
Annalisa Conversano, Alf Onshuus, Sergei Starchenko
In this paper we completely characterize solvable real Lie groups definable in o-minimal expansions of the real field.
Decomposable ordered groups
Eliana Barriga, Alf Onshuus, Charles Steinhorn
Decomposable ordered structures were introduced in \cite{OnSt} to develop a general framework to study `finite-dimensional' totally ordered structures. This paper continues this wo…
Additivity of the dp-rank
Itay Kaplan, Alf Onshuus, Alexander Usvyatsov
The main result of this article is sub-additivity of the dp-rank. We also show that the study of theories of finite dp-rank can not be reduced to the study of its dp-minimal types,…
The algebraic numbers definable in various exponential fields
Jonathan Kirby, Angus Macintyre, Alf Onshuus
We prove the following theorems: Theorem 1: For any E-field with cyclic kernel, in particular or the Zilber fields, all real abelian algebraic numbers are pointwise def…
Orthogonality and domination in unstable theories
Alf Onshuus, Alex Usvyatsov
In the first part of the paper we study orthogonality, domination, weight, regular and minimal types in the contexts of rosy and super-rosy theories. Then we try to develop analogo…
Minimal types in super-dependent theories
Assaf Hasson, Alf Onshuus
We give necessary and sufficient geometric conditions for a theory definable in an o-minimal structure to interpret a real closed field. The proof goes through an analysis of thorn…
Unstable structures definable in o-minimal theories
Assaf Hasson, Alf Onshuus
Let M be an o-minimal structure with elimination of imaginaries, N an unstable structure definable in M. Then there exists X, interpretable in N, such that X with all the structure…
One dimensional structures in o-minimal theories
Assaf Hasson, Alf Onshuus, Ya'acov Peterzil
We prove the Zil'ber Trichotomy Principle for all 1-dimensional structures which are definable in o-minimal ones. In particular, we show that any stable 1-dimensional structure is…
th-Forking, Algebraic Independence and Examples of Rosy Theories
Alf Onshuus
In a previous paper we developed the notions of th-independence and þ-ranks which define a geometric independence relation in a class of theories which we called ``rosy''. We prove…
Properties and Consequences of th-Independence
Alf Onshuus
We develop a new notion of independence suggested by Scanlon (th-independence). We prove that in a large class of theories (which includes all simple theories) this notion has many…