Smooth approximations and CSPs over finitely bounded homogeneous structures

Abstract

We introduce the novel machinery of smooth approximations, and apply it to confrm the CSP dichotomy conjecture for frst-order reducts of the random tournament, and to give new short proofs of the conjecture for various homogeneous graphs including the random graph (STOC'11, ICALP'16), and for expansions of the order of the rationals (STOC'08). Apart from obtaining these dichotomy results, we show how our new proof technique allows to unify and signifcantly simplify the previous results from the literature. For all but the last structure, we moreover characterize for the frst time those CSPs which are solvable by local consistency methods, again using the same machinery.