Related papers: Universal models and definability
In this paper a systematic study of the category GTS of generalized topological spaces (in the sense of H. Delfs and M. Knebusch) and their strictly continuous mappings begins. Some completeness and cocompleteness results are achieved.…
In this paper we will see deductive systems for classical propositional and predicate logic in the calculus of structures. Like sequent systems, they have a cut rule which is admissible. In addition, they enjoy a top-down symmetry and some…
Turing machines and spin models share a notion of universality according to which some simulate all others. Is there a theory of universality that captures this notion? We set up a categorical framework for universality which includes as…
We show that various classical theorems of real/complex linear incidence geometry, such as the theorems of Pappus, Desargues, M\"obius, and so on, can be interpreted as special cases of a single "master theorem" that involves an arbitrary…
In this paper we use the notion of Grothendieck topology to present a unified way to approach representability in supergeometry, which applies to both the differential and algebraic settings.
We study the question of whether a given regular language of finite trees can be defined in first-order logic. We develop an algebraic approach to address this question and we use it to derive several necessary and sufficient conditions for…
We study necessary conditions on the geometry and the topology of domains in $\mathbb{R}^2$ that support a positive solution to a classical overdetermined elliptic problem. The ideas and tools we use come from constant mean curvature…
A standard form of analysis for linguistic typology is the universal implication. These implications state facts about the range of extant languages, such as ``if objects come after verbs, then adjectives come after nouns.'' Such…
We shall discuss cosmological models in extended theories of gravitation. We shall define a surface, called the model surface, in the space of observable parameters which characterises families of theories. We also show how this surface can…
We combine the concepts of modal logics and many-valued logics in a general and comprehensive way. Namely, given any finite linearly ordered set of truth values and any set of propositional connectives defined by truth tables, we define the…
In this preprint we present an outline of the multidimensional version of topological Galois theory. The theory studies topological obstruction to solvability of equations "in finite terms" (i.e. to their solvability by radicals, by…
Continuous first-order logic is used to apply model-theoretic analysis to analytic structures (e.g. Hilbert spaces, Banach spaces, probability spaces, etc.). Classical computable model theory is used to examine the algorithmic structure of…
Several machine learning models are defined for inputs of any size, such as graphs with different numbers of nodes and point clouds containing varying numbers of points. The universality properties of such any-dimensional models remain…
We present a embedding of Lewis Deontic logics in PUC-Logic. We achieve this by representing the vary basic $\boldsymbol{CO}$ logic and showing its relative completeness.
We survey some results on the structure of the groups which are definable in theories of fields involved in the applications of model theory to Diophantine geometry. We focus more particularly on separably closed fields of finite degree of…
In \cite{Lyon24} the question of the decidability of quasi-dense modal logics is answered, and an upper bound in $\EXPSPACE$ is given. Unfortunately, authors' intricate proof seems to contain a major flaw that cannot be fixed, leaving the…
Universal representation of geometric patterns of disordered matters is investigated with the aid of general topology. By utilizing the result obtained in the previous study (S. Ohmori, et.al., Phys. Scr. 94, 105213 (2019)) that any…
We give a model-theoretic characterization of the class of geometric theories classified by an atomic topos having enough points; in particular, we show that every complete geometric theory classified by an atomic topos is countably…
We survey the logical structure of constructive set theories and point towards directions for future research. Moreover, we analyse the consequences of being extensible for the logical structure of a given constructive set theory. We…
In this paper, we have obtained a generalization of the Grothendieck's theorem for the space of continuous mappings $C_{\lambda,\mu}(X,Y)$ where $Y$ is a complete uniform space with the uniformity $\mu$ endowed with the topology of uniform…