Descriptive choice principles and how to separate them

N.J.H. Wontner, L. Wansner

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. 

Advanced Studies: Euro-Tbilisi Mathematical Journal, Vol. 18(3) (2025), pp. 155-171