Related papers: The amalgamation property and Urysohn structures i…

We prove an algebraic decomposition theorem for the unit group $\mathrm{GL}(R)$ of an arbitrary non-discrete irreducible, continuous ring $R$ (in von Neumann's sense), which entails that every element of $\mathrm{GL}(R)$ is both a product…

We study isometric $G$-spaces and the question of when their maximal equivariant compactification is the Gromov compactification (meaning that it coincides with the compactification generated by the distance functions to points). Answering…

We study the isomorphism relation on Borel classes of locally compact Polish metric structures. We prove that isomorphism on such classes is always classifiable by countable structures (equivalently: Borel reducible to graph isomorphism),…

We show that certain classes of modules have universal models with respect to pure embeddings. $Theorem.$ Let $R$ be a ring, $T$ a first-order theory with an infinite model extending the theory of $R$-modules and $K^T=(Mod(T), \leq_{pp})$…

Every homomorphism from finite index subgroups of a universal lattices to mapping class groups of orientable surfaces (possibly with punctures), or to outer automorphism groups of finitely generated nonabelian free groups must have finite…

We examine properties of generic automorphisms of the random poset, with the goal of explicitly characterizing them. We associate to each automorphism an auxiliary first-order structure, consisting of the random poset equipped with an…

We generalize pp elimination for modules, or more generally abelian structures, to a continuous logic environment where the abelian structure is equipped with a homomorphism to a compact (Hausdorff) group. We conclude that the continuous…

Gromov asked what a typical (finitely presented) group looks like, and he suggested a way to make the question precise in terms of limiting density. The typical finitely generated group is known to share some important properties with the…

We present a comprehensive theory of boundedness properties for Polish groups developed with a main focus on Roelcke precompactness (precompactness of the lower uniformity) and Property (OB) (boundedness of all isometric actions on…

We give a new proof of the fact that finite bipartite graphs cannot be axiomatized by finitely many first-order sentences among FINITE graphs. (This fact is a consequence of a general theorem proved by L. Ham and M. Jackson, and the…

We prove that for a number of ultrahomogeneous structures $M$, including those with the free amalgamation property, the powers of the automorphism group ${\rm{Aut}}(M)^n$, $n=1,2,\ldots$, and the group $L_0({\rm{ Aut}}(M))$ of measurable…

We devise a fairly general sufficient condition ensuring that the endomorphism monoid of a countably infinite ultrahomogeneous structure (i.e. a Fra\"{\i}ss\'{e} limit) embeds all countable semigroups. This approach provides us not only…

In this article we prove that every automorphism of a universal sofic group is class preserving, i.e. preserves the conjugacy classes

P\l onka sums consist of a general construction that provides structural description for algebras in regularized varieties, whose examples range from Clifford semigroups to many algebras of logic including involutive bisemilattices, Bochvar…

The problem addressed is the classification up to conjugation of the finite subgroups of the (classical) Morava stabilizer group S_n and the extended Morava stabilizer group G_n(u) associated to a formal group law F of height n over the…

We show that constructible models of arbitrary complete continuous first-order theories are unique up to isomorphism.

Let $M$ be a Fra\"{i}ss\'{e} structure (a countably infinite ultrahomogeneous structure). We refer to the class of structures embeddable in $M$ as the $\omega$-age of $M$. We consider the following two properties of $M$: we say that $M$ has…

We show that pseudovarieties of finitely generated algebras, i.e., classes $C$ of finitely generated algebras closed under finite products, homomorphic images, and subalgebras, can be described via a uniform structure $U$ on the free…

Let $G\subset GL(V)$ be a linear Lie group with Lie algebra $\frak g$ and let $A(\frak g)^G$ be the subalgebra of $G$-invariant elements of the associative supercommutative algebra $A(\frak g)= S(\frak g^*)\otimes \La(V^*)$. To any…

A condition, in two variants, is given such that if a property P satisfies this condition, then every logic which is at least as strong as first-order logic and can express P fails to have the compactness property. The result is used to…