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  1. Are There Enough Injective Sets?Peter Aczel, Benno Berg, Johan Granström & Peter Schuster - 2013 - Studia Logica 101 (3):467-482.
    The axiom of choice ensures precisely that, in ZFC, every set is projective: that is, a projective object in the category of sets. In constructive ZF (CZF) the existence of enough projective sets has been discussed as an additional axiom taken from the interpretation of CZF in Martin-Löf’s intuitionistic type theory. On the other hand, every non-empty set is injective in classical ZF, which argument fails to work in CZF. The aim of this paper is to shed some light on (...)
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  • A Generalized Cut Characterization of the Fullness Axiom in CZF.Laura Crosilla, Erik Palmgren & Peter Schuster - 2013 - Logic Journal of the IGPL 21 (1):63-76.
    In the present note, we study a generalization of Dedekind cuts in the context of constructive Zermelo–Fraenkel set theory CZF. For this purpose, we single out an equivalent of CZF's axiom of fullness and show that it is sufficient to derive that the Dedekind cuts in this generalized sense form a set. We also discuss the instance of this equivalent of fullness that is tantamount to the assertion that the class of Dedekind cuts in the rational numbers, in the customary (...)
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  • Refinement is Equivalent to Fullness.Albert Ziegler - 2010 - Mathematical Logic Quarterly 56 (6):666-669.
    In the article [4], a new constructive set theoretic principle called Refinement was introduced and analysed. While it seemed to be significantly weaker than its alternative, the more established axiom of Fullness , it was shown to suffice to imply many of the mathematically important consequences. In this article, we will define for each set A a set of truth values which measures the complexity of the equality relation on A. Using these sets we will show that Refinement is actually (...)
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