相关论文: Grzegorczyk sequence

The article offers a fresh perspective on Grzegorczyk logic Grz, introducing a simplified axiomatization and extending the analysis to its natural modal extensions, Grz.2 and Grz.3. I develop a control statement theory for these logics,…

Presburger arithmetic is the first-order theory of the natural numbers with addition (but no multiplication). We characterize sets that can be defined by a Presburger formula as exactly the sets whose characteristic functions can be…

We study real numbers defined by multidimensional automatic arrays weighted by multiplicatively independent bases. Let $a_1, \dots, a_r\geq 2$ be integers such that $\log a_1, \dots, \log a_r$ are $\mathbb Q$-linearly independent. Given…

Consider a sequence of real-valued functions of a real variable given by a homogeneous linear recursion with differentiable coefficients. We show that if the functions in the sequence are differentiable, then the sequence of derivatives…

The problem of algebraic dependence of solutions to (non-linear) first order autonomous equations over an algebraically closed field of characteristic zero is given a `complete' answer, obtained independently of model theoretic results on…

We present a first-order theory of sequences with integer elements, Presburger arithmetic, and regular constraints, which can model significant properties of data structures such as arrays and lists. We give a decision procedure for the…

In the first part we associate a periodic sequence to a partition and study the connection the distribution of elements of uniform limit of the sequences. Then some facts of statistical independence of these limits are proved

We introduce a class of convolutions on arithmetical functions that are regular in the sense of of Narkiewicz, homogeneous in the sense of Burnett et al, and bounded, in the sense that there exists a common finite bound for the rank of…

We consider extensions of the language of Peano arithmetic by transfinitely iterated truth definitions satisfying uniform Tarskian biconditionals. Without further axioms, such theories are known to be conservative extensions of the original…

In this paper, we consider the general divisor functions over Piatetski-Shapiro sequences. We can give some general results which contain some special divisor functions. Precisely, we extend the divisor problem over Piatetski-Shapiro…

The arithmetic of natural numbers has a natural and simple encoding within sets, and the simplest set whose structure is not that of any natural number extends this set-theoretic representation to positive and negative integers. The…

Let G be the space of generating functions of a periodic infinite order linear recurrence. In this paper we provide an explicit procedure for computing a basis of G.

In this work we extend our study on a link between automaticity and certain algebraic power series over finite fields. Our starting point is a family of sequences in a finite field of characteristic $2$, recently introduced by the first…

In this paper, we study representations of the rational Cherednik algebra associated to the complex reflection group $G_4$. In particular, we classify the irreducible finite dimensional representations and compute their characters.

Let $G$ be a group and $G_0 \subseteq G$ be a subset. A sequence over $G_0$ means a finite sequence of terms from $G_0$, where the order of elements is disregarded and the repetition of elements is allowed. A product-one sequence is a…

The notion of 'bifurcating continued fractions' is introduced. Two coupled sequences of non-negative integers are obtained from an ordered pair of positive real numbers in a manner that generalizes the notion of continued fractions. These…

In this paper we develop general techniques for classes of computable real numbers generated by subsets of total computable (recursive functions) with special restrictions on basic operations in order to investigate the following problems:…

In the base phi representation any natural number is written uniquely as a sum powers of the golden mean with digits 0 and 1, where one requires that the product of two consecutive digits is always 0. In this paper we give precise…

We present new proofs of eight integral representations of the Catalan numbers. Then, we create analogous integral representations of the Motzkin numbers and obtain new results. Most integral representations of counting sequences found in…

Throughout history, recreational mathematics has always played a prominent role in advancing research. Following in this tradition, in this paper we extend some recent work with crazy sequential representations of numbers- equations made of…