Related papers: On sequential theorems in Reverse Mathematics
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 examine the convergence properties of sequences of nonnegative real numbers that satisfy a particular class of recursive inequalities, from the perspective of proof theory and computability theory. We first establish a number of results…
A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…
We study the reverse mathematics of interval orders. We establish the logical strength of the implications between various definitions of the notion of interval order. We also consider the strength of different versions of the…
The classical rearrangement inequality provides bounds for the sum of products of two sequences under permutations of terms and show that similarly ordered sequences provide the largest value whereas opposite ordered sequences provide the…
Representation theorems relate seemingly complex objects to concrete, more tractable ones. In this paper, we take advantage of the abstraction power of category theory and provide a general representation theorem for a wide class of…
It is a striking fact from reverse mathematics that almost all theorems of countable and countably representable mathematics are equivalent to just five subsystems of second order arithmetic. The standard view is that the significance of…
A provenance analysis for a query evaluation or a model checking computation extracts information on how its result depends on the atomic facts of the model or database. Traditional work on data provenance was, to a large extent, restricted…
The bivariate difference field provides an algebraic framework for a sequence satisfying a recurrence of order two. Based on this, we focus on sequences satisfying a recurrence of higher order, and consider the multivariate difference…
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…
We study the properties of the third order sequence $(w_n)=\left(w_n(a,b,c; r, s,t)\right)$ defined by the recurrence relation $w_n = rw_{n - 1} + sw_{n - 2} + tw_{n - 3}\, (n \ge 3)$ with $w_0 = a,\,w_1 = b,\,w_2=c$, where $a$, $b$, $c$,…
Monadic second order logic is the expansion of first order logic by quantifiers ranging over unary relations. We study the shared monadic second order theory of finite linear orders, i.e. the pseudofinite monadic second order theory of…
This paper proposes new derivations of three well-known sorting algorithms, in their functional formulation. The approach we use is based on three main ingredients: first, the algorithms are derived from a simpler algorithm, i.e. the…
In many instances in first order logic or computable algebra, classical theorems show that many problems are undecidable for general structures, but become decidable if some rigidity is imposed on the structure. For example, the set of…
Sequential propositional logic deviates from ordinary propositional logic by taking into account that during the sequential evaluation of a propositional statement,atomic propositions may yield different Boolean values at repeated…
The work considers a system of fractional order partial differential equations. The existence and uniqueness theorems for the classical solution of initial-boundary value problems are proved in two cases: 1) the right-hand side of the…
We consider a system of differential equations and obtain its solutions with exponential asymptotics and analyticity with respect to the spectral parameter. Solutions of such type have importance in studying spectral properties of…
Recurrence equations have played a central role in static cost analysis, where they can be viewed as abstractions of programs and used to infer resource usage information without actually running the programs with concrete data. Such…
Consistent answers to a query from a possibly inconsistent database are answers that are simultaneously retrieved from every possible repair of the database. Repairs are consistent instances that minimally differ from the original…
In this paper we consider a class of boundary value problems for third order nonlinear functional differential equation. By the reduction of the problem to operator equation we establish the existence and uniqueness of solution and…