On a partition calculus of partial orders

On a partition calculus ofpartial ordersTam as atraiM Alfred Renyi InstituteStarkvilleMarch 20, 2010www.renyi.hu/ matraitonoo::ooooooooooo:ooooooooooolo:The purposetheory of co nal similarity types;Tukey reductions: Moore-Smith convergence;topological aspects of the theory;combinatorial aspects of the theory.pDѤ¤:Ѥ¤qloDooooooo:oooo:oo¤qoooooooooooãonDpp:¤Ñ¤qco nally similar: R; u.d.p.o. set,P;Q R into co nal subsetsTukey reducible: P Q if g : Q P,Tg maps co nal subsets to co nal subsetsEasy observations:P, Q are co nally similar if and only if P Q, i.e.TP Q and Q PT TP Q if and only if f : P Q,Tf maps unbounded subsets to unbounded subsetsCo nal typesP; , Q; upward directed partially ordered setsp¤D¤¤qã:ÑDloÑooooooo¤qoooo¤oo¤qooooooooooo¤onDpp:Ñ::Tukey reducible: P Q if g : Q P,Tg maps co nal subsets to co nal subsetsEasy observations:P, Q are co nally similar if and only if P Q, i.e.TP Q and Q PT TP Q if and only if f : P Q,Tf maps unbounded subsets to unbounded subsetsCo nal typesP; , Q; upward directed partially ordered setsco nally similar: R; u.d.p.o. set,P;Q R into co nal subsetsÑѤѤq:¤:¤lo¤oooooooooooDoo¤qooooooooooo:on:pãDpD¤qpEasy observations:P, Q are co nally similar if and only if P Q, i.e.TP Q and Q PT TP Q if and only if f : P Q,Tf maps unbounded subsets to unbounded subsetsCo nal typesP; , Q; upward directed partially ...