Related papers: Infintesimals in a Recursively Enumerable Prime Mo…
We consider systems of recursively defined combinatorial structures. We give algorithms checking that these systems are well founded, computing generating series and providing numerical values. Our framework is an articulation of the…
We give an almost entirely model-theoretic account of both Ramsey classes of finite structures and of generalized indiscernibles as studied in special cases in (for example) [7], [9]. We understand "theories of indiscernibles" to be special…
We describe a framework for systematic enumeration of families combinatorial structures which possess a certain regularity. More precisely, we describe how to obtain the differential equations satisfied by their generating series. These…
We construct the ordinary irreducible representations of the group of automorphisms of a finite rooted tree and we get a natural parametrization of them. To achieve this goals, we introduce and study the combinatorics of tree compositions,…
In this paper we prove an extreme value law for a stochastic process obtained by iterating the R\'enyi map $x \mapsto \beta x \pmod 1$, where we assume that $\beta>1$ is an integer. Haiman (2018) derived a recursion formula for the Lebesgue…
We extend Berge's Maximum Theorem to allow for incomplete preferences. We first provide a simple version of the Maximum Theorem for convex feasible sets and a fixed preference. Then, we show that if, in addition to the traditional…
We prove results concerning the representation of a given distribution by means of a given random quantity. The existence of a solution to this problem is related to the notion of conglomerability, originally introduced by Dubins to study…
Alpoge and Granville (separately) gave novel proofs that the primes are infinite that use Ramsey Theory. In particular, they use Van der Waerden's Theorem and some number theory. We prove the primes are infinite using an easier theorem from…
A new elementary proof of the prime number theorem presented recently in the framework of a scale invariant extension of the ordinary analysis is re-examined and clarified further. Both the formalism and proof are presented in a much more…
The purpose of this paper is to build an algebraic framework suited to regularise branched structures emanating from rooted forests and which encodes the locality principle. This is achieved by means of the universal properties in the…
In intuitionistic mathematics, the Brouwer Continuity Theorem states that all total real functions are (uniformly) continuous on the unit interval. We study this theorem and related principles from the point of view of Reverse Mathematics…
We introduce the notion of limiting theories, giving examples and providing a sufficient condition under which the first order theory of a structure is the limit of the first order theories of a collection of substructures. We also give a…
Solomonoff unified Occam's razor and Epicurus' principle of multiple explanations to one elegant, formal, universal theory of inductive inference, which initiated the field of algorithmic information theory. His central result is that the…
The first author introduced a sequence of polynomials (\cite{8}, sequence A174531) defined recursively. One of the main results of this study is proof of the integrality of its coefficients.
According to the math tea argument, there must be real numbers that we cannot describe or define, because there are uncountably many real numbers, but only countably many definitions. And yet, the existence of pointwise-definable models of…
Algorithmic theories of randomness can be related to theories of probabilistic sequence prediction through the notion of a predictor, defined as a function which supplies lower bounds on initial-segment probabilities of infinite sequences.…
We identify a number of decidable and undecidable fragments of first-order concatenation theory. We also give a purely universal axiomatization which is complete for the fragments we identify. Furthermore, we prove some normal-form results.
In previous papers on this project a general static logical framework for formalizing and mechanizing set theories of different strength was suggested, and the power of some predicatively acceptable theories in that framework was explored.…
Wooley ({\em J. Number Theory}, 1996) gave an elementary proof of a Bezout like theorem allowing one to count the number of isolated integer roots of a system of polynomial equations modulo some prime power. In this article, we adapt the…
An elliptic divisibility sequence, generated by a point in the image of a rational isogeny, is shown to possess a uniformly bounded number of prime terms. This result applies over the rational numbers, assuming Lang's conjecture, and over…