Related papers: Nonstandard Analysis and Constructivism!

This paper relates comparative belief structures and a general view of belief management in the setting of deductively closed logical representations of accepted beliefs. We show that the range of compatibility between the classical…

We investigate different set-theoretic constructions in Residuated Logic based on Fitting's work on Intuitionistic Set Theory. We start by stating some results concerning constructible sets within valued models of Set Theory. We present two…

We will establish the Caffarelli-Kohn-Nirenberg type inequalities with non-doubling weights being permitted. The classical Caffarelli-Kohn-Nirenberg type inequalities are categorized into non-critical and critical cases, and it is known…

Construction grammar posits that constructions, or form-meaning pairings, are acquired through experience with language (the distributional learning hypothesis). But how much information about constructions does this distribution actually…

We prove some constructive results that on first and maybe even on second glance seem impossible.

We present axioms for the real numbers by omitting the field axioms and then derive the field properties of the real numbers. We prove all our theorems constructively.

In a forthcoming book, professional computer scientist and physicist Paul Budnik presents an exposition of classical mathematical theory as the backdrop to an elegant thesis: we can interpret any model of a formal system of Peano Arithmetic…

Combining additive models and neural networks allows to broaden the scope of statistical regression and extend deep learning-based approaches by interpretable structured additive predictors at the same time. Existing attempts uniting the…

We present a theory of information expressed solely in terms of which transformations of physical systems are possible and which are impossible - i.e. in constructor-theoretic terms. Although it includes conjectured laws of physics that are…

In literature, many important combinatorial properties of subsets of N have been studied both with nonstandard techniques and from the point of view of N. In this thesis we mix these two different approaches in a technique that, at the same…

The behaviors of various confidence/credible interval constructions are explored, particularly in the region of low statistics where methods diverge most. We highlight a number of challenges, such as the treatment of nuisance parameters,…

Meta-analytic methods may be used to combine evidence from different sources of information. Quite commonly, the normal-normal hierarchical model (NNHM) including a random-effect to account for between-study heterogeneity is utilized for…

In 2011, Wooten introduced Non-Response Analysis the founding theory in Implicit Regression where Implicit Regression treats the variables implicitly as codependent variables and not as an explicit function with dependent or independent…

This work was intended to be an attempt to introduce the meta-language for working with multiple-conclusion inference rules that admit asserted propositions along with the rejected propositions. The presence of rejected propositions, and…

While most network embedding techniques model the proximity between nodes in a network, recently there has been significant interest in structural embeddings that are based on node equivalences, a notion rooted in sociology: equivalences or…

Using the functional interpretation from proof theory, we analyze nonconstructive proofs of several central theorems about polynomial and differential polynomial rings. We extract effective bounds, some of which are new to the literature,…

This document comes as supplementary material of the paper Stability in Gagliardo-Nirenberg inequalities by the same authors. It is intended to state a number of classical or elementary statements concerning constants and inequalities for…

Behavioral research can provide important insights for SE practices. But in performing it, many studies of SE are committing a normative fallacy - they misappropriate normative and prescriptive theories for descriptive purposes. The…

Model-theoretic frameworks for Nonstandard Analysis depend on the existence of nonprincipal ultrafilters, a strong form of the Axiom of Choice (AC). Hrbacek and Katz, APAL 72 (2021) formulate axiomatic nonstandard set theories SPOT and SCOT…

This note has two principal aims: to portray an essence of Non-Standard Analysis as a particular structure (which we call lim-rim), noting its interplay with the notion of ultrapower, and to present a construction of Non-Standard Analysis,…