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Constructive Set Theory and Brouwerian Principles [PDF]

, 2020
JUCS - Journal of Universal Computer Science Volume Nr.
Michael Rathjen
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Formalizing Abstract Algebra in Constructive Set Theory [PDF]

, 2003
We present a machine-checked formalization of elementary abstract algebra in constructive set theory. Our formalization uses an approach where we start by specifying the group axioms as a collection of inference rules, defining a logic for groups. Then we can tell whether a given set with a binary operation is a group or not, and derive all properties ...
Xin Yu, Hickey, Jason
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EXACT COMPLETION AND CONSTRUCTIVE THEORIES OF SETS [PDF]

The Journal of Symbolic Logic, 2020
AbstractIn the present paper we use the theory of exact completions to study categorical properties of small setoids in Martin-Löf type theory and, more generally, of models of the Constructive Elementary Theory of the Category of Sets, in terms of properties of their subcategories of choice objects (i.e., objects satisfying the axiom of choice ...
Jacopo Emmenegger, Erik Palmgren
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Logics and admissible rules of constructive set theories

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2023
We survey the logical structure of constructive set theories and point towards directions for future research. Moreover, we analyse the consequences of being extensible for the logical structure of a given constructive set theory. We finally provide examples of a number of set theories that are extensible.
Rosalie Iemhoff, Robert Paßmann
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Families of Sets in Constructive Measure Theory [PDF]

, 2022
We present the first steps of a predicative reconstruction of the constructive Bishop-Cheng measure theory. Working in a semi-formal elaboration of Bishop's set theory and invoking the notion of a set-indexed family of subsets (of a given set), we arrive at notions of a pre-integration space and of a pre-measure space.
Max Zeuner
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VERY LARGE SET AXIOMS OVER CONSTRUCTIVE SET THEORIES [PDF]

The Bulletin of Symbolic Logic
Abstract We investigate large set axioms defined in terms of elementary embeddings over constructive set theories, focusing on $\mathsf {IKP}$ and $\mathsf {CZF}$ . Most previously studied large set axioms, notably, the constructive analogues of large cardinals below $0^\sharp
Hanul Jeon, R. G. Matthews
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Synthetic Dimensions in Constructive Set Theory

This paper explores the novel concept of "synthetic dimensions" within the framework of constructive set theory. While synthetic dimensions have gained prominence in physics, particularly in condensed matter systems where additional spatial or internal degrees of freedom are engineered, their rigorous and foundational treatment within constructive ...
SÉRGIO DE ANDRADE, PAULO
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A cumulative hierarchy of sets for constructive set theory [PDF]

Mathematical Logic Quarterly, 2014
The von Neumann hierarchy of sets is heavily used as a basic tool in classical set theory, being an underlying ingredient in many proofs and concepts. In constructive set theories like without the powerset axiom however, it loses much of its potency by ceasing to be a hierarchy of sets as its single stages become only classes. This article proposes an
Albert Ziegler
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Constructive mathematics - its set theory and practice

, 1974
The thesis falls naturally into two parts, in the first of which (comprising Chapter 1) there is laid down a set-theoretic foundation for constructive mathematics as understood by Errett Bishop and his followers. The work of this part closely follows the lines of the corresponding classical development of set theory by Anthony Morse, highlights several
Douglas Bridges
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Quotient topologies in constructive set theory and type theory

Annals of Pure and Applied Logic, 2005
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hajime Ishihara, Erik Palmgren
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