Martin-Lof randomness, invariant measures and countable homogeneous structurs

2012/05/02 by Fouche, Willem L.
#FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.1205.0386

Abstract

We use ideas from topological dynamics (amenability), combinatorics (structural Ramsey theory) and model theory (Fra" iss' e 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-L" of random, of 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-L" of random.

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