Related papers: Randomness below complete theories of arithmetic
The notion of weak truth-table reducibility plays an important role in recursion theory. In this paper, we introduce an elaboration of this notion, where a computable bound on the use function is explicitly specified. This elaboration…
Let $d,n\in \mathbb{N}$ be such that $d=\omega(1)$, and $d\le n^{1-a}$ for some constant $a>0$. Consider a $d$-regular graph $G=(V, E)$ and the random graph process that starts with the empty graph $G(0)$ and at each step $G(i)$ is obtained…
Represented as graphs, real networks are intricate combinations of order and disorder. Fixing some of the structural properties of network models to their values observed in real networks, many other properties appear as statistical…
We generalize the optimal coupling theorem to multiple random variables: Given a collection of random variables, it is possible to couple all of them so that any two differ with probability comparable to the total-variation distance between…
A semi-measure is a generalization of a probability measure obtained by relaxing the additivity requirement to super-additivity. We introduce and study several randomness notions for left-c.e. semi-measures, a natural class of effectively…
We prove the classification of joinings for maximal horospherical subgroups acting on homogeneous spaces without any restriction on the characteristic. Using the linearization technique we deduce a special case of Raghunathan's orbit…
We optimize multiway equijoins on relational tables using degree information. We give a new bound that uses degree information to more tightly bound the maximum output size of a query. On real data, our bound on the number of triangles in a…
We give an explicit description of the Lie algebra of derivations for a class of infinite dimensional algebras which are given by \'etale descent. The algebras under consideration are twisted forms of central algebras over rings, and…
We study the continuity properties of trajectories for some random series of functions $\sum a\_kf(\alpha X\_k(\omega))$ where $a\_k$ is a complex sequence, $X\_k$ a sequence of real independent random variables, $f$ is a real valued…
We introduce a class of real algebraic varieties characterised by a simple rationality condition, which exhibit strong properties regarding approximation of continuous and smooth mappings by regular ones. They form a natural counterpart to…
We characterize the strength, in terms of Weihrauch degrees, of certain problems related to Ramsey-like theorems concerning colourings of the rationals and of the natural numbers. The theorems we are chiefly interested in assert the…
We study and describe possibilities for arities of elementary theories and of their expansions. Links for arities with respect to Boolean algebras, to disjoint unions and to compositions of structures are shown. The dynamics for arities of…
We introduce a new way of quantifying the degrees of incompatibility of two ob- servables in a probabilistic physical theory and, based on this, a global measure of the degree of incompatibility inherent in such theories, across all…
We study links between first-order formulas and arbitrary properties for families of theories, classes of structures and their isomorphism types. Possibilities for ranks and degrees for formulas and theories with respect to given properties…
By employing certain extended classical summation theorems, several surprising \pi and other formulae are displayed.
The main purpose of this paper is to prove that the positive real numbers can be decomposed into finitely many disjoint pieces which are also closed under addition and multiplication. As a byproduct of the argument we determine all the…
In this paper we characterize the congruence associated to the direct sum of all irreducible representations of a finite semigroup over an arbitrary field, generalizing results of Rhodes for the field of complex numbers. Applications are…
We extend in a natural way the operation of Turing machines to infinite ordinal time, and investigate the resulting supertask theory of computability and decidability on the reals. The resulting computability theory leads to a notion of…
Nonuniformity is a central concept in computational complexity with powerful connections to circuit complexity and randomness. Nonuniform reductions have been used to study the isomorphism conjecture for NP and completeness for larger…
We prove the existence of complexified real arrangements with the same combinatorics but different embeddings in the complex projective plane. Such pair of arrangements has an additional property: they admit conjugated equations on the ring…