Groups of order-automorphisms of the rationals with prescribed scale type

Peter J. Cameron*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)

Abstract

It is shown that, for any given m and n with m < n (where n = ∞ is allowed), there is a group of order-preserving permutations of the rational numbers whose degrees of homogeneity and uniqueness are m and n, respectively. This is in contrast with the situation for the real numbers. The result is deduced from a more general theorem applying to a wide class of relational structures. The tools used are Fraïssé's theorem on homogeneous structures and a lemma of Tits. All the groups constructed are isomorphic to the free group of countable rank.

Original languageEnglish
Pages (from-to)163-171
Number of pages9
JournalJournal of Mathematical Psychology
Volume33
Issue number2
DOIs
Publication statusPublished - 1 Jan 1989

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