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Let $\Gamma$ be an LCA group and $(\mu_n)$ be a sequence of bounded regular Borel measures on $\Gamma$ tending to a measure $\mu_0$. Let $G$ be the dual group of $\Gamma$, $S$ be a non-empty subset of $G \setminus \{ 0 \}$, and $[{\mathcal…
Given a finite Borel measure $\mu$ on R n and basic semi-algebraic sets $\Omega$\_i $\subset$ R n , i = 1,. .. , p, we provide a systematic numerical scheme to approximate as closely as desired $\mu$(\cup\_i $\Omega$\_i), when all moments…
We deal with the systematic development of stability for the context of approximate elementary submodels of a monster metric space, which is not far, but still very distinct from the first order case. In particular we prove the analogue of…
Let $\mathscr{M}$ be a monoidal model category that is also combinatorial and left proper. If $\mathscr{O}$ is a monad, operad, properad, or a PROP; following Segal's ideas we develop a theory of Quillen-Segal $\mathscr{O}$-algebras and…
Given a countable o-minimal theory T, we characterize the Borel complexity of isomorphism for countable models of T up to two model-theoretic invariants. If T admits a nonsimple type, then it is shown to be Borel complete by embedding the…
Given Polish space $\mathcal{Y}$ and a continuous language $L$ we study the corresponding logic $\mathsf{Iso}(\mathcal{Y})$-space $\mathcal{Y}_L$. We build a framework of generalized model theory towards analysis of Borel complexity of…
We investigate the descriptive complexity of the set of models of first-order theories. Using classical results of Knight and Solovay, we give a sharp condition for complete theories to have a $\pmb\Pi_\omega^0$-complete set of models. In…
We examine domain-valued maxitive measures defined on the Borel subsets of a topological space. Several characterizations of regularity of maxitive measures are proved, depending on the structure of the topological space. Since every…
R.D.Mauldin asked if every translation invariant $\sigma$-finite Borel measure on $\RR^d$ is a constant multiple of Lebesgue measure. The aim of this paper is to show that the answer is "yes and no", since surprisingly the answer depends on…
The trivial proof of the ergodic theorem for a finite set $Y$ and a permutation $T:Y\to Y$ shows that for an arbitrary function $f:Y\to{\mathbb R}$ the sequence of ergodic means $A_n(f,T)$ stabilizes for $n \gg |T|$. We show that if $|Y|$…
We study models M of set theory that are "condensable", in the sense that there is an "ordinal" v of M such that the rank initial segment of M determined by v is both isomorphic to M, and also an elementary submodel of M for infinitary…
We import the algebro-geometric notion of a complete collineation into the study of maximum likelihood estimation in directed Gaussian graphical models. A complete collineation produces a perturbation of sample data, which we call a…
One of Courcelle's celebrated results states that if C is a class of graphs of bounded tree-width, then model-checking for monadic second order logic is fixed-parameter tractable on C by linear time parameterised algorithms. An immediate…
We first partly develop a mathematical notion of stable consistency intended to reflect the actual consistency property of human beings. Then we give a generalization of the first and second G\"odel incompleteness theorem to stably…
We define and investigate HC-forcing invariant formulas of set theory, whose interpretations in the hereditarily countable sets are well behaved under forcing extensions. This leads naturally to a notion of cardinality ||Phi|| for sentences…
We consider a generic class of log-concave, possibly random, (Gibbs) measures. We prove the concentration of an infinite family of order parameters called multioverlaps. Because they completely parametrise the quenched Gibbs measure of the…
The class of generic structures among those consisting of the measure algebra of a probability space equipped with an automorphism is axiomatizable by positive sentences interpreted using an approximate semantics. The separable generic…
We show that the regularity of monomial ideals whose associated prime ideals are totally ordered by inclusion is linearly bounded.
Let K be an algebraically bounded structure and T be its theory. If T is model complete, then the theory of K endowed with a derivation, denoted by $T^{\delta}$, has a model completion. Additionally, we prove that if the theory T is…
In 2008, Loday shed light on the existence of Hopf-Boreltheorems for operads. Using the vocabulary of category theory, Livernet,Mesablishvili and Wisbauer extended such theorems to monads. In bothcases, the reasoning was to start from a…