An uncountable Furstenberg–Zimmer structure theory

Abstract Furstenberg–Zimmer structure theory refers to the extension of dichotomy between compact and weakly mixing parts a measure-preserving dynamical system algebraic geometric descriptions such conditional setting, where is established relative factor analogs those are sought. Although unconditional characterizations known for arbitrary systems, situation understood under certain countability separability hypotheses on underlying groups spaces. The aim this article remove these restrictions in establish full generality. As an independent byproduct, we connection analysis systems ergodic internal logic Boolean topoi.