Related papers: Higher amalgamation properties in stable theories
We study topological group theoretic properties of algebraic groups over local fields. In particular, we find conditions under which such groups have closed images under arbitrary continuous homomorphisms into arbitrary topological groups.
We show that a finite collection of stable subgroups of a finitely generated group has finite height, finite width and bounded packing. We then use knowledge about intersections of conjugates to characterize finite families of…
We show that the theories of partially ordered sets, lattices, semilattices, Boolean algebras, Heyting algebras with a further coarser partial order, or a linearization, or an auxiliary relation have the strong amalgamation property,…
We characterize when the elementary diagram of a mutually algebraic structure has a model complete theory, and give an explicit description of a set of existential formulas to which every formula is equivalent. This characterization yields…
We explore the N=1* theories compactified on a circle with twisted boundary conditions. The gauge algebra of these theories are the so-called twisted affine Lie algebra. We propose the exact superpotentials by guessing the sum of all…
We show that the class of C*-algebras with stable rank greater than a given positive integer is axiomatizable in logic of metric structures. As a consequence we show that the stable rank is continuous with respect to forming ultrapowers of…
In this paper, it is shown that a topological space $X$ is compact iff every maximal ideal of the power set ring $\mathcal{P}(X)$ converges to exactly one point of $X$. Then as an application, simple and ring-theoretic proofs are provided…
We prove that many seemingly simple theories have Borel complete reducts. Specifically, if a countable theory has uncountably many complete 1-types, then it has a Borel complete reduct. Similarly, if $Th(M)$ is not small, then $M^{eq}$ has…
Tate cohomology has been generalised by several authors using different constructions that have applications in group theory, ring theory and homotopical algebra. Therefore, there is a need for a uniform account that explains why their…
We prove a converse Lyapunov theorem for almost sure stabilizability and almost sure asymptotic stabilizability of controlled diffusions: given a stochastic system a.s. stochastic open loop stabilizable at the origin, we construct a lower…
RO*-algebras are defined and studied. For RO*-algebra T, using properties of partial order, it is established that the set of bounded elements can be endowed with C*-norm. The structure of commutative subalgebras of T is considered and the…
A new reference state for density functional theory, termed the independent atom ansatz, is introduced in this work. This ansatz allows for the exact representation of electron density in terms of non-interacting, atom-localized orbitals.…
We seek to create tools for a model-theoretic analysis of types in algebraically closed valued fields (ACVF). We give evidence to show that a notion of 'domination by stable part' plays a key role. In Part A, we develop a general theory of…
We present a system of axioms motivated by a topological intuition: The set of subsets of any set is a topology on that set. On the one hand, this system is a common weakening of Zermelo-Fraenkel set theory ZF, the positive set theory GPK…
We introduce an abstract framework to study certain classes of stably embedded pairs of models of a complete $\mathcal{L}$-theory $T$, called \textit{beautiful pairs}, which comprises Poizat's belles paires of stable structures and van den…
In this paper we generalize the algebraic density property to not necessarily smooth affine varieties relative to some closed subvariety containing the singular locus. This property implies the remarkable approximation results for…
We recover the rays in the tensor product of Hilbert spaces within a larger class of so called `states of compoundness', structured as a complete lattice with the `state of separation' as its top element. At the base of the construction…
We make two contributions to the study of theory combination in satisfiability modulo theories. The first is a table of examples for the combinations of the most common model-theoretic properties in theory combination, namely stable…
We study when a union of saturated models is saturated in the framework of tame abstract elementary classes (AECs) with amalgamation. We prove: $\mathbf{Theorem}$ If $K$ is a tame AEC with amalgamation satisfying a natural definition of…
An overview is given of the various expansions of fields and fusions of strongly minimal sets obtained by means of Hrushovski's amalgamation method, as well as a characterization of the groups definable in these structures.