On an open problem of Amadio and Curien: The finite antichain condition (Q2573335)

The authors show that for any \(\omega\)-algebraic meet-cpo \(D\), if all higher-order stable function spaces built from \(D\) are \(\omega\)-algebraic, then \(D\) is finitary. This result is half job of solving the open question whether the category of stable bifinite domains of Amadio-Droste is the largest cartesian closed full sub-category of the category of \(\omega\)-algebraic meet-cpos with stable functions.