Title

A Canonical Countryman Line

Publication Date

5-2007

Type of Culminating Activity

Thesis

Degree Title

Master of Science in Mathematics

Department

Mathematics

Major Advisor

Justin Tatch Moore

Abstract

The objective of this thesis is to give a novel proof that the uncountable linear order C(ρ0) is a Countryman line using an innovative presentation of the full lower trace from Todorcevic's method of minimal walks. In order to motivate the subject we will explicate the basis problem for the class of uncountable linear orders and prove several facts indicating the intrinsic interest of Countryman lines. In order to facilitate the proof we will give a short primer on the method of minimal walks.

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