Order Types and Similarity Transformations
Seymour Ginsburg · Transactions of the American Mathematical Society · 1955
Suppose that a and p. are two distinct order types for which a <p(2).The question of the existence of an order type t for which a<r<p is hereafter referred to as "problem P." Whenever such an order type r exists we shall say problem P admits of a solution.The two purposes of this paper are (a) to study the order types of simply ordered sets of solutions to problem P, as applied to the cases where (I) <x is any linear order type and p. =X(3), and (II) (r = 0, p, is any linear order type of power 2N°, and t is of power 2N»; and (b) to study pairs of simply ordered sets whose symmetric difference contains just two elements and whose order types are incomparable.(') By 0 is meant the smallest ordinal number whose power is 2Ko.(8) By/-1 is meant the inverse function of/.