Yatir Halevi

activity

20152026

most citedA Conjectural Classification of Strongly Dependent Fields

10 citations · 20 across the 19 of their papers we have counts for

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26 papers · 1 filter

math.LO2026

On differentiability in weakly o-minimal expansions of fields

Juan Pablo Acosta, Yatir Halevi, Assaf Hasson +2

We show that every definable function in a weakly o-minimal expansion of a field $K$ is generically differentiable, where the derivative takes values in the Cauchy completion of $K…

math.LO2026

A note on uniform finiteness in weakly o-minimal theories

Yatir Halevi, Assaf Hasson, Ya'acov Peterzil

For an $ℵ_{0}$ -saturated weakly o-minimal expansion of an ordered group $M$ , it is shown that $M^{eq}$ has uniform finiteness if and only if the colle…

math.LO2026

Model-theoretic Tameness in finite extensions of groups

Yatir Halevi, Saharon Shelah

It is shown that finite-index extensions and finite-index subgroups of $ω$ -stable groups can be model-theoretically wild. More precisely, there exists an $ω$ -stable group $G$ such…

math.LO2025

The infinitesimal subgroup of interpretable groups in some dp-minimal valued fields

Yatir Halevi, Assaf Hasson, Ya'acov Peterzil

We continue our local analysis of groups interpretable in various dp-minimal valued fields, as introduced in [8]. We associate with every infinite group $G$ interpretable in those…

math.LO2024

Infinite Cliques in Simple and Stable Graphs

Yatir Halevi, Itay Kaplan, Saharon Shelah

Suppose that $G$ is a graph of cardinality $μ^{+}$ with chromatic number $χ (G) \geq μ^{+}$ . One possible reason that this could happen is if $G$ contains a clique of size $μ^{+}$ . We prov…

math.LO2024★ 1 cited

The classification of dp-minimal integral domains

Christian d'Elbée, Yatir Halevi, Will Johnson

We classify dp-minimal integral domains, building off the existing classification of dp-minimal fields and dp-minimal valuation rings. We show that if R is a dp-minimal integral do…

math.LO2023

Semisimple groups interpretable in various valued fields

Yatir Halevi, Assaf Hasson, Ya'acov Peterzil

We study infinite groups interpretable in power bounded $T$ -convex, $V$ -minimal or $p$ -adically closed fields. We show that if $G$ is an interpretable definably semisimple group (i…

math.LO2023

Contracting Endomorphisms of Valued Fields

Yuval Dor, Yatir Halevi

We prove that the class of separably algebraically closed valued fields equipped with a distinguished Frobenius endomorphism $x \mapsto x^{q}$ is decidable, uniformly in $q$ . The res…

math.LO2023

Models of Abelian varieties over valued fields, using model theory

Yatir Halevi

Given an elliptic curve $E$ over a perfect defectless henselian valued field $(F, val)$ with perfect residue field $k_{F}$ and valuation ring $O_{F}$ , there…

math.LO2022

Definably semisimple groups interpretable in $p$ -adically closed fields

Yatir Halevi, Assaf Hasson, Ya'acov Peterzil

Let $K$ be a $p$ -adically closed field and $G$ a group interpretable in $K$ . We show that if $G$ is definably semisimple (i.e. $G$ has no definable infinite normal abelian subgroup…

math.LO2022

On groups interpretable in various valued fields

Yatir Halevi, Assaf Hasson, Ya'acov Peterzil

We study infinite groups interpretable in three families of valued fields: $V$ -minimal, power bounded $T$ -convex, and $p$ -adically closed fields. We show that every such group $G$ …

math.LO2022

Enriching a predicate and tame expansions of the integers

Gabriel Conant, Christian d'Elbée, Yatir Halevi +2

Given a structure $M$ and a stably embedded $\emptyset$ -definable set $Q$ , we prove tameness preservation results when enriching the induced structure on $Q$ by some furt…

math.LO2021

Saturated Models for the Working Model Theorist

Yatir Halevi, Itay Kaplan

We put in print a classical result that states that for most purposes, there is no harm in assuming the existence of saturated models in model theory. The presentation is aimed for…

math.LO2021

Interpretable Fields in Various Valued Fields

Yatir Halevi, Assaf Hasson, Ya'acov Peterzil

Let $K = (K, v, \dots)$ be a dp-minimal expansion of a non-trivially valued field of characteristic $0$ and $F$ an infinite field interpretable in $K$ . A…

math.LO2021★ 2 cited

Fields interpretable in $P$ -minimal fields

Yatir Halevi, Assaf Hasson, Ya'acov Peterzil

We prove that an infinite field interpretable in a $p$ -adically closed field $K$ is definably isomorphic to a finite extension of $K$ . The result remains true in any $P$ -minimal fi…

math.LO2021

Infinite Stable Graphs With Large Chromatic Number II

Yatir Halevi, Itay Kaplan, Saharon Shelah

We prove a version of the strong Taylor's conjecture for stable graphs: if $G$ is a stable graph whose chromatic number is strictly greater than $ℶ_{2} (ℵ_{0})$ then $G$ contai…

math.LO2020

Infinite Stable Graphs With Large Chromatic Number

Yatir Halevi, Itay Kaplan, Saharon Shelah

We prove that if $G = (V, E)$ is an $ω$ -stable (respectively, superstable) graph with $χ (G) > ℵ_{0}$ (respectively, $2^{ℵ_{0}}$ ) then $G$ contains all the finite subgraphs of the…

math.LO2020

Dp-minimal integral domains

Christian d'Elbée, Yatir Halevi

It is shown that every dp-minimal integral domain $R$ is a local ring and for every non-maximal prime ideal $p$ of $R$ , the localization $R_{p}$ is a valuatio…

math.LO2019

Definable V-topologies, Henselianity and NIP

Yatir Halevi, Assaf Hasson, Franziska Jahnke

We initiate the study of definable V-topolgies and show that there is at most one such V-topology on a t-henselian NIP field. Equivalently, we show that if $(K, v_{1}, v_{2})$ is a bi-va…

math.LO2018★ 10 cited

A Conjectural Classification of Strongly Dependent Fields

Yatir Halevi, Assaf Hasson, Franziska Jahnke

We survey the history of Shelah's conjecture on strongly dependent fields, give an equivalent formulation in terms of a classification of strongly dependent fields and prove that t…

math.LO2017★ 6 cited

The dp-rank of abelian groups

Yatir Halevi, Daniel Palacín

An equation to compute the dp-rank of any abelian group is given. It is also shown that its dp-rank, or more generally that of any one-based group, agrees with its Vapnik-Chervonen…

math.LO2017

Eliminating Field Quantifiers in Strongly Dependent Henselian Fields

Yatir Halevi, Assaf Hasson

We prove elimination of field quantifiers for strongly dependent henselian fields in the Denef-Pas language. This is achieved by proving the result for a class of fields generalizi…

math.LO2017

Strongly Dependent Ordered Abelian Groups and Henselian Fields

Yatir Halevi, Assaf Hasson

Strongly dependent ordered abelian groups have finite dp-rank. They are precisely those groups with finite spines and $∣ {p prime : [G : pG] = \infty} ∣ < \infty$ . We apply this to…

math.LO2016

On Stably Pointed Varieties and Generically Stable Groups in ACVF

Yatir Halevi

We give a geometric description of the pair $(V, p)$ , where $V$ is an affine algebraic variety over a non-trivially valued algebraically closed field $K$ with valuation ring $\mathc…

On differentiability in weakly o-minimal expansions of fields

A note on uniform finiteness in weakly o-minimal theories

Model-theoretic Tameness in finite extensions of groups

The infinitesimal subgroup of interpretable groups in some dp-minimal valued fields

Infinite Cliques in Simple and Stable Graphs

The classification of dp-minimal integral domains

Semisimple groups interpretable in various valued fields

Contracting Endomorphisms of Valued Fields

Models of Abelian varieties over valued fields, using model theory

Definably semisimple groups interpretable in p-adically closed fields

On groups interpretable in various valued fields

Enriching a predicate and tame expansions of the integers

Saturated Models for the Working Model Theorist

Interpretable Fields in Various Valued Fields

Fields interpretable in P-minimal fields

Infinite Stable Graphs With Large Chromatic Number II

Infinite Stable Graphs With Large Chromatic Number

Dp-minimal integral domains

Definable V-topologies, Henselianity and NIP

A Conjectural Classification of Strongly Dependent Fields

The dp-rank of abelian groups

Eliminating Field Quantifiers in Strongly Dependent Henselian Fields

Strongly Dependent Ordered Abelian Groups and Henselian Fields

On Stably Pointed Varieties and Generically Stable Groups in ACVF

Definably semisimple groups interpretable in $p$ -adically closed fields

Fields interpretable in $P$ -minimal fields