Canonical partitions

摘要

In this thesis we investigate edge and k-tuple partitions of countable relational structures. So far Ramsey properties for very few countable relational structures have been investigated. Except for some very simple countable relational structures, like the complete graph on $omega$-vertices, we know that in general the Ramsey arrow relation ${cal A}to({cal A})sbsp{n}{cal C}$ does not hold.;But, a slightly more general relation seems to hold in many cases. Namely in many cases it turned out that, for given ${cal A}$ and ${cal C},$ there is a number m such that for all numbers n the following relation holds:$${cal A}to({cal A})sbsp{n/m}{cal C}.$$.;In this thesis we investigate this phenomenon more generally by proposing in Chapter 2 a framework in which to work. We then apply this framework to several special cases.