Descriptive Choice Principles and How to Separate Them
Lucas Wansner, Ned J H Wontner
TL;DR
This paper introduces a separation technique for descriptive choice principles using Jensen forcing, expanding on Kanovei's theorem, and clarifies the relationships among various descriptive choice axioms.
Contribution
It develops a new method based on Jensen forcing to distinguish between different descriptive choice principles, generalizing previous results by Kanovei.
Findings
Established a separation technique for descriptive choice principles
Generalized Kanovei's theorem using Jensen forcing
Clarified the hierarchy of descriptive choice axioms
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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Taxonomy
TopicsDecision-Making and Behavioral Economics · Game Theory and Voting Systems · Epistemology, Ethics, and Metaphysics