相关论文: A computable version of Hall's Harem Theorem and G…

We prove a new version of Hall's Harem Theorem, where the final matching is realized by a unary function with additional conditions on behavior of cycles. The present paper can be considered as a helpful companion of the paper of the…

We prove a computable version of Hall's Harem Theorem and apply it to computable versions of Tarski's alternative theorem.

We prove a Montel theorem for Hilbert space valued functions, and a non-commutative version of this theorem, by composing with unitaries to achieve convergence.

While there is a well-established notion of what a computable ordinal is, the question which functions on the countable ordinals ought to be computable has received less attention so far. We propose a notion of computability on the space of…

We establish a computable version of Gelfand Duality. Under this computable duality, computably compact presentations of metrizable spaces uniformly effectively correspond to computable presentations of unital commutative $C^*$ algebras.

According to Haar's Theorem, every compact group $G$ admits a unique (regular, right and) left-invariant Borel probability measure $\mu_G$. Let the Haar integral (of $G$) denote the functional $\int_G:\mathcal{C}(G)\ni f\mapsto \int…

We show that the theory of the partial order of computably enumerable equivalence relations (ceers) under computable reduction is 1-equivalent to true arithmetic. We show the same result for the structure comprised of the dark ceers and the…

Some mathematical theorems represent ideas that are discovered again and again in different forms. One such theorem is Hall's marriage theorem. This theorem is equivalent to several other theorems in combinatorics and optimization theory,…

We explore new connections between the fields and local observables in two dimensional chiral conformal field theory. We show that in a broad class of examples, the von Neumann algebras of local observables (a conformal net) can be obtained…

This paper shows how to use Computational Algebra techniques, namely the decomposition of rational functions in one variable, to explore a certain set of modular functions, called replicable functions, that arise in Monstrous Moonshine. In…

Using an iterative tree construction we show that for simple computable subsets of the Cantor space Hausdorff, constructive and computable dimensions might be incomputable.

The desirable gambles framework provides a foundational approach to imprecise probability theory but relies heavily on linear utility assumptions. This paper introduces function-coherent gambles, a generalization that accommodates…

Computational properties of the Hahn-Banach theorem have been studied in computable, constructive and reverse mathematics and in all these approaches the theorem is equivalent to weak K\H{o}nig's lemma. Gherardi and Marcone proved that this…

The purpose of this article is to relate coarse cohomology of metric spaces with a more computable cohomology. We introduce a notion of boundedly supported cohomology and prove that coarse cohomology of many spaces are isomorphic to the…

Frames play an important role in various practical problems related to signal and image processing. In this paper, we define computable frames in computable Hilbert spaces and obtain computable versions of some of their characterizations.…

We extend the classical Mercer theorem to reproducing kernel Hilbert spaces whose elements are functions from a measurable space $X$into $\mathbb C^n$. Given a finite measure $\mu$ on $X$, we represent the reproducing kernel $K$ as…

In this paper we investigate algorithmic randomness on more general spaces than the Cantor space, namely computable metric spaces. To do this, we first develop a unified framework allowing computations with probability measures. We show…

We introduce computable actions of computable groups and prove the following versions of effective Birkhoff's ergodic theorem. Let $\Gamma$ be a computable amenable group, then there always exists a canonically computable tempered two-sided…

We provide a simple proof of a computable analogue to the Jayne Rogers Theorem from descriptive set theory. The difficulty of the proof is delegated to a simulation result pertaining to non-deterministic type-2 machines. Thus, we…

Under natural conditions (such as split property and geometric modular action of wedge algebras) it is shown that the unitary equivalence class of the net of local (von Neumann) algebras in the vacuum sector associated to double cones with…