Multiplicative posets

A functionf from the posetP to the posetQ is a strict morphism if for allx, y P withx we havef(x). If there is such a strict morphism fromP toQ we writeP Q, otherwise we writePQ. We say a posetM is multiplicative if for any posetsP, Q withPM andQM we haveP ×QM. (Here (p₁,q₁)<(p₂,q₂) if and only ifp₁<p₂ andq₁<q₂.) This paper proves that well-founded trees with height are multiplicative posets.This research was supported in part by NSERC Grant #69-1325.