Related papers: A comparison of minimal systems for constructive a…
In this article, we construct empirical likelihood (EL)-weighted estimators of linear functionals of a probability measure in the presence of side information. Motivated by nuisance parameters in semiparametric models with possibly infinite…
Exponential-constructible functions are an extension of the class of constructible functions. This extension was formulated by Cluckers-Loeser in the context of semi-algebraic and sub-analytic structures, when they studied stability under…
This paper gives two different proofs to a structural theorem of decreasing minimization (lexicographic optimization) on integrally convex sets. The theorem states that the set of decreasingly minimal elements of an integrally convex set…
We develop a novel formal theory of finite structures, based on a view of finite structures as a fundamental artifact of computing and programming, forming a common platform for computing both within particular finite structures, and in the…
The formal system lambda-delta is a typed lambda calculus that pursues the unification of terms, types, environments and contexts as the main goal. lambda-delta takes some features from the Automath-related lambda calculi and some from the…
The inferential model (IM) approach, like fiducial and its generalizations, depends on a representation of the data-generating process. Here, a particular variation on the IM construction is considered, one based on generalized…
We describe a class of sharply o-minimal structures, called analytically generated structures, whose definable sets and their complexity filtration are determined by the collection of definable complex cells. We prove a polynomially…
The minimum classical extension S$^{+g}$ of a classically sound theory S based on intuitionistic logic, defined by adding to S the Gentzen negative interpretations of its mathematical axioms, contains a faithful translation S$^g$ of the…
This book is an introductory course to basic commutative algebra with a particular emphasis on finitely generated projective modules, which constitutes the algebraic version of the vector bundles in differential geometry. We adopt the…
A new constructivist approach to modeling in economics and theory of consciousness is proposed. The state of elementary object is defined as a set of its measurable consumer properties. A proprietor's refusal or consent for the offered…
We introduce a reducibility on classes of structures, essentially a uniform enumeration reducibility. This reducibility is inspired by the Friedman-Stanley paper on using Borel reductions to compare classes of countable structures. This…
In 2002 Robert Solovay proved that a subsystem BI of classical second order arithmetic, with bar induction and arithmetical countable choice, can be negatively interpreted in the neutral subsystem BSK of Kleene's intuitionistic analysis FIM…
We continue the development of the theory of construction schemes over $\omega_1$ as introduced by the third author by studying their relation with forcing axioms. Formally, we introduce the cardinals $\mathfrak{m}^n_{\mathcal{F}}$ and use…
An inferential model (IM) is a model describing the construction of provably reliable, data-driven uncertainty quantification and inference about relevant unknowns. IMs and Fisher's fiducial argument have similar objectives, but a…
Canonical inference rules and canonical systems are defined in the framework of non-strict single-conclusion sequent systems, in which the succeedents of sequents can be empty. Important properties of this framework are investigated, and a…
Bourke and Garner described how to cofibrantly generate algebraic weak factorisation systems by a small double category of morphisms. However they did not give an explicit construction of the resulting factorisations as in the classical…
We deal with the random combinatorial structures called assemblies. By weakening the logarithmic condition which assures regularity of the number of components of a given order, we extend the notion of logarithmic assemblies. Using the…
This paper deals with certain fundamental results about affine hulls and simplices in a real normed linear space. The framework of the paper is Bishop's constructive mathematics, which, with its characteristic interpretation of existence as…
A folded type model is developed for analyzing compositional data. The proposed model involves an extension of the $\alpha$-transformation for compositional data and provides a new and flexible class of distributions for modeling data…
This paper describes an axiomatic theory BT for constructive mathematics. BT has a predicative comprehension axiom for a countable number of set types and usual combinatorial operations. BT has intuitionistic logic, is consistent with…