Martin-Lof randomness, invariant measures and countable homogeneous structurs [article]

Willem L. Fouche
2012 arXiv   pre-print
We use ideas from topological dynamics (amenability), combinatorics (structural Ramsey theory) and model theory (Fraïssé limits) to study closed amenable subgroups G of the symmetric group S_∞ of a countable set, where S_∞ has the topology of pointwise convergence. We construct G-invariant measures on the universal minimal flows associated with these groups G in, moreover, an algorithmic manner. This leads to an identification of the generic elements, in the sense of being Martin-Löf random, of
more » ... these flows with respect to the constructed invariant measures. Along these lines we study the random elements of S_∞, which are permutations that transform recursively presented universal structures into such structures which are Martin-Löf random.
arXiv:1205.0386v1 fatcat:cvlnun5ppfcbzdzipteldkmvgi