94 citations · 314 across the 26 of their papers we have counts for
31 papers · 1 filter
Globally valued fields: foundations
Itaï Ben Yaacov, Pablo Destic, Ehud Hrushovski +1
We present foundations for globally valued fields, a class of enriched fields capturing some aspects of the geometry of global fields, based on the product formula. We show that th…
Extremal models and direct integrals in affine logic
Itaï Ben Yaacov, Tomás Ibarlucía, Todor Tsankov
Affine logic is a fragment of continuous logic, introduced by Bagheri, in which only affine functions are allowed as connectives. This has the effect of endowing type spaces with t…
Globally valued function fields: existential closure
Itaï Ben Yaacov, Ehud Hrushovski
These notes form part of a joint research project on the logic of fields with many valuations, connected by a product formula. We define such structures and name them {\em globally…
On the expressive power of quantifiers in continuous logic
Itaï Ben Yaacov
In this short note we compare the expressive power of real-valued continuous logic (or just continuous logic, in recent literature) with that of compact-valued continuous logic, pr…
Star sorts, Lelek fans, and the reconstruction of non--categorical theories in continuous logic
Itaï Ben Yaacov
We prove a reconstruction theorem valid for arbitrary theories in continuous (or classical) logic in a countable language, that is to say that we provide a complete bi-interpretati…
A metric version of Schlichting's Theorem
Itaï Ben Yaacov, Frank Olaf Wagner
If F is a type-definable family of commensurable subsets, subgroups or sub-vector spaces in a metric structure, then there is an invariant subset, subgroup or sub-vector space comm…
Eberlein oligomorphic groups
Itaï Ben Yaacov, Tomás Ibarlucía, Todor Tsankov
We study the Fourier--Stieltjes algebra of Roelcke precompact, non-archimedean, Polish groups and give a model-theoretic description of the Hilbert compactification of these groups…
On Roeckle-precompact Polish group which cannot act transitively on a complete metric space
Itaï Ben Yaacov
We study when a continuous isometric action of a Polish group on a complete metric space is, or can be, transitive. Our main results consist of showing that certain Polish groups,…
Metric Scott analysis
Itai Ben Yaacov, Michal Doucha, Andre Nies +1
We develop an analogue of the classical Scott analysis for metric structures and infinitary continuous logic. Among our results are the existence of Scott sentences for metric stru…
Isometrisable group actions
Itaï Ben Yaacov, Julien Melleray
Given a separable metrisable space X, and a group G of homeomorphisms of X, we introduce a topological property of the action of G on X which is equivalent to the existence of a G-…
Reconstruction of separably categorical metric structures
Itaï Ben Yaacov, Adriane Kaïchouh
We extend Ahlbrandt and Ziegler's reconstruction results to the metric setting: we show that separably categorical metric structures are determined, up to bi-interpretability, by t…
Weakly almost periodic functions, model-theoretic stability, and minimality of topological groups
Itaï Ben Yaacov, Todor Tsankov
We investigate the automorphism groups of -categorical structures and prove that they are exactly the Roelcke precompact Polish groups. We show that the theory of a stru…
Model theoretic stability and definability of types, after A. Grothendieck
Itaï Ben Yaacov
We point out how the "Fundamental Theorem of Stability Theory", namely the equivalence between the "non order property" and definability of types, proved by Shelah in the 1970s, is…
An independence theorem for NTP2 theories
Itaï Ben Yaacov, Artem Chernikov
We establish several results regarding dividing and forking in NTP2 theories. We show that dividing is the same as array-dividing. Combining it with existence of strictly invariant…
The linear isometry group of the Gurarij space is universal
Itaï Ben Yaacov
We give a construction of the Gurarij space, analogous to Katetov's construction of the Urysohn space. The adaptation of Katetov's technique uses a generalisation of the Arens-Eell…
Fraïssé limits of metric structures
Itaï Ben Yaacov
We develop \emph{Fraïssé theory}, namely the theory of \emph{Fraïssé classes} and \emph{Fraïssé limits}, in the context of metric structures. We show that a class of finitely gener…
Grey subsets of Polish spaces
Itaï Ben Yaacov, Julien Melleray
We develop the basics of an analogue of descriptive set theory for functions on a Polish space . We use this to define a version of the small index property in the context of Po…
Lipschitz functions on topometric spaces
Itaï Ben Yaacov
We study functions on topometric spaces which are both (metrically) Lipschitz and (topologically) continuous, using them in contexts where, in classical topology, ordinary continuo…
On uniform canonical bases in lattices and other metric structures
Itaï Ben Yaacov
We discuss the notion of \emph{uniform canonical bases}, both in an abstract manner and specifically for the theory of atomless lattices. We also discuss the connection betwe…
Polish topometric groups
Itaï Ben Yaacov, Alexander Berenstein, Julien Melleray
We define and study the notion of \emph{ample metric generics} for a Polish topological group, which is a weakening of the notion of ample generics introduced by Kechris and Rosend…
Model theoretic properties of metric valued fields
Itaï Ben Yaacov
We study model theoretic properties of valued fields (equipped with a real-valued multiplicative valuation), viewed as metric structures in continuous first order logic. For techni…
Almost indiscernible sequences and convergence of canonical bases
Itaï Ben Yaacov, Alexander Berenstein, C. Ward Henson
We give a model-theoretic account for several results regarding sequences of random variables appearing in Berkes & Rosenthal \cite{Berkes-Rosenthal:AlmostExchangeableSequences}. I…
Continuous first order logic for unbounded metric structures
Itaï Ben Yaacov
We present an adaptation of continuous first order logic to unbounded metric structures. This has the advantage of being closer in spirit to C. Ward Henson's logic for Banach space…
A proof of completeness for continuous first-order logic
Itaï Ben Yaacov, Arthur Paul Pedersen
The primary purpose of this article is to show that a certain natural set of axioms yields a completeness result for continuous first-order logic. In particular, we show that in co…