Related papers: Internal Categoricity and the Generic Multiverse
We prove a Generic Vanishing Theorem for coherent sheaves on an abelian variety over an algebraically closed field $k$. When $k=\CC$ this implies a conjecture of Green and Lazarsfeld.
We present generalized algebraic theories corresponding to slightly modified versions of two of the type theories in our paper Type Theory with Explicit Universe Polymorphism. We first present a generalized algebraic theory for categories…
Classical analysis of variance requires that model terms be labeled as fixed or random and typically culminate by comparing variability from each batch (factor) to variability from errors; without a standard methodology to assess the…
We define the notion of a multi-sorted algebraic theory, which is a generalization of an algebraic theory in which the objects are of different "sorts." We prove a rigidification result for simplicial algebras over these theories, showing…
During the study of the topic of limit summability of functions (introduced by the author in 2001), we encountered some types of functions that are related to the mean value theorem. In this paper, we formally define mean value and…
The main aim of this paper is to present the ideas which lead first to the solution of the unitarizability problem for $\GL(n)$ over nonarchimedean local fields and to the recognition that the same result holds over archimedean local…
Category theory unifies mathematical concepts, aiding comparisons across structures by incorporating objects and morphisms, which capture their interactions. It has influenced areas of computer science such as automata theory, functional…
Multi-view clustering (MVC) aims at exploring category structures among multi-view data in self-supervised manners. Multiple views provide more information than single views and thus existing MVC methods can achieve satisfactory…
In this article ideas from Kit Fine's theory of arbitrary objects are applied to questions regarding mathematical structuralism. I discuss how sui generic mathematical structures can be viewed as generic systems of mathematical objects,…
Although the categorical arithmetic is not effectively axiomatizable, the belief that the incompleteness Theorems can be apply to it is fairly common. Furthermore, the so-called "essential" (or "inherent") semantic incompleteness of the…
Categorical compositional distributional semantics (CCDS) allows one to compute the meaning of phrases and sentences from the meaning of their constituent words. A type-structure carried over from the traditional categorial model of grammar…
We investigate an extension of ZFC set theory (in an extended language) that stipulates the existence of a proper class of indiscernibles over the universe. One of the main results of the paper shows that the purely set-theoretical…
The problem is posed of establishing a possible relationship between a new type of Multi-verse representation, G\"odel undecidability theorems and the logic of classical, quantum mechanics and quantum gravity. For this purpose example cases…
Recently in \cite{FM, FlMo}, the language of MV-algebras was extended by adding a unary operation, an internal operator, called also a state-operator. In \cite{DD1}, a stronger version of state MV-algebras, called state-morphism MV-algebras…
Measurability with respect to ideals is tightly connected with absoluteness principles for certain forcing notions. We study a uniformization principle that postulates the existence of a uniformizing function on a large set, relative to a…
This paper develops a categorical framework to clarify the relationship between the completeness and compactness theorems in classical first-order logic. Rather than claiming that different model constructions yield naturally isomorphic…
This paper investigates some issues arising in categorical models of reversible logic and computation. Our claim is that the structural (coherence) isomorphisms of these categorical models, although generally overlooked, have decidedly…
General Relativity is not the definitive theory of Gravitation due to several shortcomings which are coming out both from theoretical and experimental viewpoints. At large scales (astrophysical and cosmological scales) the attempts to match…
Argumentation theory is a powerful paradigm that formalizes a type of commonsense reasoning that aims to simulate the human ability to resolve a specific problem in an intelligent manner. A classical argumentation process takes into account…
These notes provide a hopefully pedagogic introduction to Born-Infeld theory and some of its uses in String/M-Theory from the perspective of some-one interested in spacetime geometry. Causality and the consequences of having both the open…