63 citations · 112 across the 14 of their papers we have counts for
15 papers
Stateful Realizers for Nonstandard Analysis
Bruno Dinis, Étienne Miquey
In this paper we propose a new approach to realizability interpretations for nonstandard arithmetic. We deal with nonstandard analysis in the context of (semi)intuitionistic realiz…
On definable Skolem functions and trichotomy
Bruno Dinis, Mário J. Edmundo
In this paper we give an explicit characterization of o-minimal structures with definable Skolem functions/definable choice. Such structures are, after naming finitely many element…
Strong convergence for the alternating Halpern-Mann iteration in CAT(0) spaces
Bruno Dinis, Pedro Pinto
In this paper we consider, in the general context of CAT(0) spaces, an iterative schema which alternates between Halpern and Krasnoselskii-Mann style iterations. We prove, under su…
Effective metastability for a method of alternating resolvents
Bruno Dinis, Pedro Pinto
A generalized method of alternating resolvents was introduced by Boikanyo and Moro{\c s}anu as a way to approximate common zeros of two maximal monotone operators. In this paper we…
On the convergence of algorithms with Tikhonov regularization terms
Bruno Dinis, Pedro Pinto
We consider the strongly convergent modified versions of the Krasnosel'ski\uı-Mann, the forward-backward and the Douglas-Rachford algorithms with Tikhonov regularization terms, int…
Parametrised Functional Interpretations
Bruno Dinis, Paulo Oliva
This paper presents a general framework for unifying functional interpretations. It is based on families of parameters allowing for different degrees of freedom on the design of th…
Quantitative results on the multi-parameters Proximal Point Algorithm
Bruno Dinis, Pedro Pinto
We give a quantitative analysis of a theorem due to Fenghui Wang and Huanhuan Cui concerning the convergence of a multi-parametric version of the proximal point algorithm. Wang and…
Metastability of the proximal point algorithm with multi-parameters
Bruno Dinis, Pedro Pinto
In this article we use techniques of proof mining to analyse a result, due to Yonghong Yao and Muhammad Aslam Noor, concerning the strong convergence of a generalized proximal poin…
Fundamental group in o-minimal structures with definable Skolem functions
Bruno Dinis, Mário J. Edmundo, Marcello Mamino
In this paper we work in an arbitrary o-minimal structure with definable Skolem functions and we prove that definably connected, locally definable manifolds are uniformly definably…
On flexible sequences
Bruno Dinis, Tran Van Nam, Imme van den Berg
In the setting of nonstandard analysis we introduce the notion of flexible sequence. The terms of flexible sequences are external numbers. These are a sort of analogue for the clas…
Old and new approaches to the Sorites paradox
Bruno Dinis
The Sorites paradox is the name of a class of paradoxes that arise when vague predicates are considered. Vague predicates lack sharp boundaries in extension and is therefore not cl…
Axiomatics for the external numbers of nonstandard analysis
Bruno Dinis, Imme van den Berg
Neutrices are additive subgroups of a nonstandard model of the real numbers. An external number is the algebraic sum of a nonstandard real number and a neutrix. Due to the stabilit…
Intuitionistic nonstandard bounded modified realisability and functional interpretation
Bruno Dinis, Jaime Gaspar
We present a bounded modified realisability and a bounded functional interpretation of intuitionistic nonstandard arithmetic with nonstandard principles. The functional interpretat…
Characterization of distributivity in a solid
Bruno Dinis, Imme van den Berg
We give a characterization of the validity of the distributive law in a solid. There exists equivalence between the characterization and the modified axiom of distibutivity valid i…
On the quotient class of non-archimedean fields
Bruno Dinis, Imme van den Berg
The quotient class of a non-archimedean field is the set of cosets with respect to all of its additive convex subgroups. The algebraic operations on the quotient class are the Mink…