Pseudo PCF

We continue our investigation on pcf with weak forms of the axiom of choice. Characteristically, we assume DC+P(Y) when looking at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\prod\nolimits_{s \in Y} {{\delta _s}} $$\end{document}. We get more parallels of pcf theorems.