Related papers: Computable paradoxical decompositions

We prove that derived equivalent algebras have isomorphic differential calculi in the sense of Tamarkin--Tsygan.

We show that Morley's theorem on the number of countable models of a countable first-order theory becomes an undecidable statement when extended to second-order logic. More generally, we calculate the number of equivalence classes of…

The Tarski number of a group $G$ is the minimal number of the pieces of paradoxical decompositions of that group. Using configurations along with a matrix combinatorial property we construct paradoxical decompositions. We also compute an…

We prove a computable version of de Finetti's theorem on exchangeable sequences of real random variables. As a consequence, exchangeable stochastic processes expressed in probabilistic functional programming languages can be automatically…

A computably presented algebraic field $F$ has a \emph{splitting algorithm} if it is decidable which polynomials in $F[X]$ are irreducible there. We prove that such a field is computably categorical iff it is decidable which pairs of…

We prove a non-minimal modularity lifting theorem for ordinary Galois representations over imaginary quadratic fields, conditional on a local-global compatibility conjecture for ordinary torsion classes.

In this paper we examine the reverse mathematical strength of a variation of Hindman's Theorem HT constructed by essentially combining HT with the Thin Set Theorem TS to obtain a principle which we call thin-HT. thin-HT says that every…

In this chapter, we explore how (Type-2) computable distributions can be used to give both (algorithmic) sampling and distributional semantics to probabilistic programs with continuous distributions. Towards this end, we sketch an encoding…

We prove Sklar's theorem in infinite dimensions via a topological argument and the notion of inverse systems.

The Isomorphism Conjectures are translated into the language of homotopical algebra, where they resemble Thomason's descent theorems.

In this article we establish novel decompositions of Gaussian fields taking values in suitable spaces of generalized functions, and then use these decompositions to prove results about Gaussian multiplicative chaos. We prove two…

We reduce the calculation of the simplest Hodge integrals to some sums over decorated trees. Since Hodge integrals are already calculated, this gives a proof of a rather interesting combinatorial theorem and a new representation of…

The Classic Howard's algorithm, a technique of resolution for discrete Hamilton-Jacobi equations, is of large use in applications for its high efficiency and good performances. A special beneficial characteristic of the method is the…

This paper describes a method used to construct infinitely many probable counterexamples of the abc conjecture over the rational integers.

We construct a fully faithful functor from the category of graphs to the category of fields. Using this functor, we resolve a longstanding open problem in computable model theory, by showing that for every nontrivial countable structure S,…

We prove that, for every theory $T$ which is given by an ${\mathcal L}_{\omega_1,\omega}$ sentence, $T$ has less than $2^{\aleph_0}$ many countable models if and only if we have that, for every $X\in 2^\omega$ on a cone of Turing degrees,…

We find an elementary proof for Voiculescu's theorem on the polar decomposition of circular variables.

Let $A$ be a finite-dimensional algebra over an algebraically closed field $\Bbbk$. For any finite-dimensional $A$-module $M$ we give a general formula that computes the indecomposable decomposition of $M$ without decomposing it, for which…

An algebraic deformation theory of coalgebra morphisms is constructed.

We give a geometric proof of the Decomposition Theorem of Beilinson, Bernstein, Deligne and Gabber for the direct image of the intersection cohomology complex under a proper map of complex algebraic varieties. The method rests on new…