TD implies CCR

TL;DR

This paper proves that under ZF set theory, Turing determinacy implies the countable choice axiom for sets of reals, establishing a logical connection between these concepts.

Contribution

It demonstrates that Turing determinacy implies CCR within ZF, revealing a new implication in set theory without the axiom of choice.

Findings

TD implies CCR under ZF

Establishes a logical link between determinacy and choice axioms

Advances understanding of set-theoretic implications of determinacy

Abstract

Assuming $\mathrm{ZF}$, we prove that Turing determinacy ($\mathrm{TD}$) implies countable choice axiom for sets of reals ($\mathrm{CCR}$).