In 1965, D. Scott proved that for every countable structure of a countable language there is a sentence of infinitary logic that describes it up to isomorphism. In order to obtain this result, Scott developed what is now known as the Scott analysis: a way of approximating the (analytic) isomorphism relation via a descending sequence of Borel equivalence relations. We present a new way of approximating abstract equivalence relations on Polish spaces that was introduced by S. Solecki and compare it with other known generalizations of Scott analysis, in particular with metric Scott analysis defined in [I. Ben Yaacov, M. Doucha, A. Nies, T. Tsankov, Metric Scott analysis, Advances in Mathematics 318 (2017) 46-87].

This is a joint work with S. Solecki and J. Swaczyna.