Trees and Linearly Ordered Sets

Abstract

This chapter presents an introduction to several problems concerning trees and linearly ordered sets and the dualities between them. Several classes of trees and linearly ordered sets are presented and considered as set-theoretical, topological, and algebraical structures in the chapter. The chapter also discusses many fundamental problems concerning trees and linearly ordered sets, which are set-theoretical in nature. Most of the problems are undecidable on the basis of the usual axioms of set theory. Thus, a great number of results presented in the chapter are consistency results.