Related papers: A Tame Generic Structure with Non-Algebraic Geomet…
Second-order superintegrable systems in dimensions two and three are essentially classified. With increasing dimension, however, the non-linear partial differential equations employed in current methods become unmanageable. Here we propose…
We present a generic construction of finite realisations of amalgamation patterns. An amalgamation pattern is specified by a finite collection of finite template structures together with a collection of partial isomorphisms between them. A…
We propose a new definition of so called Hamiltonian forms in n-plectic geometry and show that they have a non-trivial Lie infinity-algebra structure.
We study covers of the multiplicative group of an algebraically closed field as quasiminimal pregeometry structures and prove that they satisfy the axioms for Zariski-like structures presented in \cite{lisuriart}, section 4. These axioms…
Using an infinitary version of the Hypergraph Removal Lemma due to Towsner, we prove a model-theoretic higher amalgamation result. In particular, we obtain an independent amalgamation property which holds in structures which are measurable…
We show that in a stable first-order theory, the failure of higher-dimensional type amalgamation can always be witnessed by algebraic structures which we call n-ary polygroupoids. This generalizes a result of Hrushovski that failures of…
We discuss in detail the parasupersymmetric quantum mechanics of arbitrary order where the parasupersymmetry is between the normal bosons and those corresponding to the truncated harmonic oscillator. We show that even though the parasusy…
Denote Hrushovski's non-collapsed ab initio construction for an $n$-ary relation by $\mathcal{M}_{\not\sim}$ and the analogous construction for a symmetric $n$-ary relation by $\mathcal{M}_{\sim}$. We show that $\mathcal{M}_{\not\sim}$ is…
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 develop some basic results about full amalgamation classes with intrinsic trascendentals. These classes have generics whose models may have finite subsets whose intrinsic closure is not contained in its algebraic closure. We will show…
Classification and invariants, with respect to basis changes, of finite dimensional algebras are considered. An invariant open, dense (in the Zariscki topology) subset of the space of structural constants is defined. The algebras with…
We introduce the concept of topological finite-determinacy for germs of analytic functions within a fixed ideal $I$, which provides a notion of topological finite-determinacy of functions with non-isolated singularities. We prove the…
We relate the existence problem of universal objects to the properties of corresponding enriched categories (lifts or expansions). In particular, extending earlier results, we prove that for every (possibly infinite) regular set F of finite…
We classify the twisted tensor products of a finite set algebra with a two elements set algebra using colored quivers obtained through considerations analogous to Ore extensions. This provides also a classification of entwining structures…
We compare two different notions of generic expansions of countable saturated structures. One kind of genericity is related to model-companions and to amalgamation constructions \'a la Hrushovski-Fra\"iss\'e. Another notion of generic…
The superamalgamation property is a strong form of the amalgamation property which applies to ordered structures; it has found many applications in algebraic logic. We show that superamalgamation has some interest also from the pure…
The recent investigation of the gauge structure of extended geometry is generalised to situations when ancillary transformations appear in the commutator of two generalised diffeomorphisms. The relevant underlying algebraic structure turns…
We explore a notion of pseudofinite dimension, introduced by Hrushovski and Wagner, on an infinite ultraproduct of finite structures. Certain conditions on pseudofinite dimension are identified that guarantee simplicity or supersimplicity…
We construct a topology on a given algebraically closed field with a distinguished subfield which is also algebraically closed. This topology is finer than Zariski topology and it captures the sets definable in the pair of algebraically…
We investigate structural implications arising from the condition that a given directed graph does not interpret, in the sense of primitive positive interpretation with parameters or orbits, every finite structure. Our results generalize…