The Axiom of Choice in computability theory and Reverse Mathematics with a cameo for the Continuum Hypothesis
The Axiom of Choice in computability theory and Reverse Mathematics with a cameo for the Continuum Hypothesis
Abstract The Axiom of Choice (${\textsf{AC}}$ for short) is the most (in)famous axiom of the usual foundations of mathematics, ${\textsf{ZFC}}$ set theory. The (non-)essential use of ${\textsf{AC}}$ in mathematics has been well-studied and thoroughly classified. Now, fragments of countable ${\textsf{AC}}$ not provable in ${\textsf{ZF}}$ have recently been used in Kohlenbach’s …