Rudimentary and arithmetical constructive set theory

Annals of Pure and Applied Logic 164 (4):396-415 (2013)
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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DOI 10.1016/j.apal.2012.10.004
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References found in this work BETA

The Fine Structure of the Constructible Hierarchy.R. Björn Jensen - 1972 - Annals of Mathematical Logic 4 (3):229-308.
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.

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