Article ID Journal Published Year Pages File Type
4665666 Advances in Mathematics 2014 27 Pages PDF
Abstract
Our result lines up with previous similar classifications for the random graph and the order of the rationals; it also provides further evidence for a conjecture due to Simon Thomas which states that the number of structures definable in a homogeneous structure in a finite relational language is, up to first-order interdefinability, always finite. In the proof we use the new technique of “canonical functions” originally invented in the context of theoretical computer science, which allows for a systematic Ramsey-theoretic analysis of functions acting on the random partial order. The technique identifies patterns in arbitrary functions on the random partial order, which makes them accessible to finite combinatorial arguments.
Related Topics
Physical Sciences and Engineering Mathematics Mathematics (General)
Authors
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