Rudimentary and arithmetical constructive set theory

Annals of Pure and Applied Logic 164 (4):396-415 (2013)
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Abstract

The aim of this paper is to formulate and study two weak axiom systems for the conceptual framework of constructive set theory . Arithmetical CST is just strong enough to represent the class of von Neumann natural numbers and its arithmetic so as to interpret Heyting Arithmetic. Rudimentary CST is a very weak subsystem that is just strong enough to represent a constructive version of Jensenʼs rudimentary set theoretic functions and their theory. The paper is a contribution to the study of formal systems for CST that capture significant stages in the development of constructive mathematics in CST

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10.1016/j.apal.2012.10.004

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Citations of this work

Constructing the constructible universe constructively.Michael Rathjen - 2024 - Annals of Pure and Applied Logic 175 (3):103392.
Constructive Ackermann's interpretation.Hanul Jeon - 2022 - Annals of Pure and Applied Logic 173 (5):103086.

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References found in this work

Constructive set theory.John Myhill - 1975 - Journal of Symbolic Logic 40 (3):347-382.
On Interpretations of Arithmetic and Set Theory.Richard Kaye & Tin Lok Wong - 2007 - Notre Dame Journal of Formal Logic 48 (4):497-510.
The fine structure of the constructible hierarchy.R. Björn Jensen - 1972 - Annals of Mathematical Logic 4 (3):229.
Some properties of intuitionistic Zermelo-Frankel set theory.John Myhill - 1973 - In A. R. D. Mathias & H. Rogers (eds.), Cambridge Summer School in Mathematical Logic. New York: Springer Verlag. pp. 206--231.

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