Chapter 10 Embeddings Of Linear Orderings And Fraisse'S Conjecture

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Particular linear orderings A and B—whether or not A ⪯ B—has been frequently asked for. This chapter undertakes a more systematic study of the ⪯ relation. Although various questions about the ⪯ relation had been considered by Dushnik and Miller, Hausdorff, Sierpinski, and others, the systematic study of the ⪯ relation on arbitrary order types began with Fraïssé, who listed a number of results he had obtained and several conjectures. As this brief article, together with the paper of Dushnik and Miller, provide the impetus for further study of the embeddability relation, it is appropriate to cite the results obtained (translating them into the terminology of this book) and the conjectures proposed. This is done in this chapter; it presents some basic concepts and derives some results about them. The additively indecomposable order types, defined below, are occasionally called indecomposable in the literature.

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