Universal lnfinite Partial Orders

Author: Johnston, John Beverley

Year: 1955

Degree: Dissertation (Ph.D.)

Advisor: Dilworth, Robert P.

Committee Member: Unknown, Unknown

Option: Mathematics; Physics

DOI: 10.7907/WSQ4-ZA23

Abstract

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.

We consider infinite partial orders in which the order or comparability relations are transitive, non-reflexive, and nonsymmetric. Our purpose is to construct for each infinite cardinal [...] a so-called [...] partial order in which every partial order of cardinality [...] can be isomorphically embedded. Using the Axiom of Choice we easily construct an [...] partial order of cardinality [...], while for those infinite cardinals [...] for which [...], the General Continuum Hypothesis enables us to construct an [...]; universal partial order of cardinality [...].

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