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Constructive set theory with Markov's principle

open access: yesConstructive set theory with Markov's principle
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The natural numbers in constructive set theory

open access: closedMathematical Logic Quarterly, 2008
AbstractConstructive set theory started with Myhill's seminal 1975 article [8]. This paper will be concerned with axiomatizations of the natural numbers in constructive set theory discerned in [3], clarifying the deductive relationships between these axiomatizations and the strength of various weak constructive set theories.
Michael Rathjen
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Hereditarily Finite Sets in Constructive Type Theory

open access: closed, 2016
We axiomatize hereditarily finite sets in constructive type theory and show that all models of the axiomatization are isomorphic. The axiomatization takes the empty set and adjunction as primitives and comes with a strong induction principle. Based on the axiomatization, we construct the set operations of ZF and develop the basic theory of finite ...
Gert Smolka, Kathrin Stark
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Constructive set theory

Journal of Symbolic Logic, 1975
This paper is the third in a series collectively entitled Formal systems of intuitionistic analysis. The first two are [4] and [5] in the bibliography; in them I attempted to codify Brouwer's mathematical practice. In the present paper, which is independent of [4] and [5], I shall do the same for Bishop's book [1].
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