Related papers: Partial Model Theory -- Ultraproducts and Compactn…
We develop a method to design tunable quasiperiodic structures of particles suspended in a fluid by controlling standing acoustic waves. One application of our results is to ultrasound directed self-assembly, which allows fabricating…
The tendency of semidefinite programs to compose perfectly under product has been exploited many times in complexity theory: for example, by Lovasz to determine the Shannon capacity of the pentagon; to show a direct sum theorem for…
We construct a model of type theory enjoying parametricity from an arbitrary one. A type in the new model is a semi-cubical type in the old one, illustrating the correspondence between parametricity and cubes. Our construction works not…
This work establishes a structure theorem for compact K\"ahler manifolds with semipositive anticanonical bundle. Up to finite \'etale cover, it is proved that such manifolds split holomorphically and isometrically as a product of Ricci flat…
We present an introduction to modern continuous model theory with an emphasis on its interactions with topics covered in this volume such as $C^*$-algebras and von Neumann algebras. The role of ultraproducts is highlighted and expositions…
In this paper we demonstrate how the recently reported exactly and quasi-exactly solvable models admitting quasinormal modes can be constructed and classified very simply and directly by the newly proposed prepotential approach. These new…
We prove analogues of several well-known results concerning rational morphisms between quadrics for the class of so-called quasilinear $p$-hypersurfaces. These hypersurfaces are nowhere smooth over the base field, so many of the geometric…
Directional notions in topology and analysis naturally lead to nonsymmetric structures such as quasi-metrics, quasi-uniformities, and modular spaces. In these settings, classical notions of connectedness and completion based on symmetric…
A description of physical reality in which wholeness is the foundation is discussed along with the motivation for such an attempt. As a possible mathematical framework within which a physical theory based on wholeness may be expressed,…
We introduce and study two new relations between function spaces over measure spaces of infinite measure, motivated by the question of establishing compactness. The first relation captures the uniform decay of function (quasi-)norms ``at…
The last half century of research into the structure, dynamics, and thermodynamics of simple liquids has revealed a number of approximate universalities. This paper argues that simple liquids' reduced-coordinate constant-potential-energy…
Given a group $G$ and a subset $X \subset G$, an element $g \in G$ is called quasi-positive if it is equal to a product of conjugates of elements in the semigroup generated by $X$. This notion is important in the context of braid groups,…
Organising the relevant literature and by letting statistical convergence play the main role in the theory of compactness, a variant of compactness called statistical compactness has been achieved. As in case of sequential compactness, one…
We turn `the' Church-Turing Hypothesis from an ambiguous source of sensational speculations into a (collection of) sound and well-defined scientific problem(s): Examining recent controversies, and causes for misunderstanding, concerning the…
We study countable embedding-universal and homomorphism-universal structures and unify results related to both of these notions. We show that many universal and ultrahomogeneous structures allow a concise description (called here a finite…
The topological interpretation of modal logics provides descriptive languages and proof systems for reasoning about points of topological spaces. Recent work has been devoted to model checking of spatial logics on discrete spatial…
Ultrafinitism postulates that we can only compute on relatively short objects, and numbers beyond certain value are not available. This approach would also forbid many forms of infinitary reasoning and allow to remove certain paradoxes…
Legacy procedures for topic modelling have generally suffered problems of overfitting and a weakness towards reconstructing sparse topic structures. With motivation from a consumer-generated corpora, this paper proposes semiparametric topic…
The main result of this paper states that for any group $G$ with an automatic structure $L$ with unique representatives one can construct a uniform partial algorithm which detects $L$-rational subgroups and gives their preimages in $L$.…
By revisiting the path-integral formulation of the Hubbard model, we propose a theoretical approach based on a semiclassical approximation employing an unconventional coherent-state representation. Within this framework, a subset of the…