A functionf from the posetP to the posetQ is a strict morphism if for allx, y ∈ P withx<y we havef(x)<f(y). If there is such a strict morphism fromP toQ we writeP → Q, otherwise we writeP\(\not \to \)Q. We say a posetM is multiplicative if for any posetsP, Q withP\(\not \to \)M andQ\(\not \to \)M we haveP ×Q\(\not \to \)M. (Here (p1,q1)<(p2,q2) if and only ifp1<p2 andq1<q2.) This paper proves that well-founded trees with height ≤ω are multiplicative posets.
Mathematics Subject Classification (1991)06A06
Key wordsPosets strict morphisms multiplicativity Hedetniemi's conjecture
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