Related papers: Universal theories and compactly expandable models
We propose a definition of quantum computable functions as mappings between superpositions of natural numbers to probability distributions of natural numbers. Each function is obtained as a limit of an infinite computation of a quantum…
We introduce a general notion of covering property, of which many classical definitions are particular instances. Notions of closure under various sorts of convergence, or, more generally, under taking kinds of accumulation points, are…
This article aims to develop a new account of scientific explanation for computer simulations. To this end, two questions are answered: what is the explanatory relation for computer simulations? and what kind of epistemic gain should be…
We examine connections between rationality of certain indefinite integrals and equilibrium of Coulomb charges in the complex plane.
Simple argument in favour of unitarity, to all orders, of space-like noncommutative theory is given.
In the past many papers have appeared which simulated surface growth with different growth models. The results showed that, if models differed only slightly in their `growth' rules, the resulting surfaces may belong to different…
We present a comprehensive survey on removability of compact plane sets with respect to various classes of holomorphic functions. We also discuss some applications and several open questions, some of which are new.
An important goal in studying the relations between unitary VOAs and conformal nets is to prove the equivalence of their ribbon categories. In this article, we prove this conjecture for many familiar examples. Our main idea is to construct…
A $\lambda$-quiddity of size $n$ is an $n$-tuple of elements from a fixed set, which is a solution to a matrix equation that arises in the study of Coxeter's friezes. The study of these solutions involves in particular the use of a notion…
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…
We explain and explore class-theoretic potentialism -- the view that one can always individuate more classes over a set-theoretic universe. We examine some motivations for class-theoretic potentialism, before proving some results concerning…
We extend a dichotomy between 1-basedness and supersimplicity proved in a previous paper. The generalization we get is to arbitrary language, with no restrictions on the topology (we do not demand type-definabilty of the open set in the…
In this paper we show that if X is an infinite compactum cleavable over an ordinal, then X must be homeomorphic to an ordinal. X must also therefore be a LOTS. This answers two fundamental questions in the area of cleavability. We also…
All constructive methods employed in modern mathematics produce only countable sets, even when designed to transcend countability. We show that any constructive argument for uncountability -- excluding diagonalization techniques --…
We formalize an existing computability-theoretic method of presenting first-order structures whose domains have the cardinality of the continuum. Work using these methods until now has emphasized their topological properties. We shift the…
This article aims at clarifying the language and practice of scientific experiment, mainly by hooking observability on calculability.
The aim of this paper is to extend the structure theory for infinitely generated modules over tame hereditary algebras to the more general case of modules over concealed canonical algebras. Using tilting, we may assume that we deal with…
We propose a list of open problems in pluripotential theory partially motivated by their applications to complex differential geometry. The list includes both local questions as well as issues related to the compact complex manifold…
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 possibility of extending operations of topological and semitopological algebras to their Stone-\v{C}ech compactification and factorization of continuous functions through homomorphisms to metrizable algebras are investigated. Most…