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Descriptive Choice Principles and How to Separate Them

Published 19 Jul 2023 in math.LO | (2307.09837v1)

Abstract: The axiom of countable choice for reals is one of the most basic fragments of the axiom of choice needed in many parts of mathematics. Descriptive choice principles are a further stratification of this fragment by the descriptive complexity of the sets. In this paper, we provide a separation technique for descriptive choice principles based on Jensen forcing. Our results generalise a theorem by Kanovei.

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