2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/121306We give a new simple proof of the decidability of the First Order Theory of (omega^omega^i,+) and the Monadic Second Order Theory of (omega^i,<), improving the complexity in both cases. Our algorithm is based on tree automata and a new representation of (sets of) ordinals by (infinite) trees.Computer Science and Game Theorytext