Tree Automata Make Ordinal Theory Easy [chapter]

Thierry Cachat
2006 Lecture Notes in Computer Science  
We give a new simple proof of the decidability of the First Order Theory of (ω ω i , +) and the Monadic Second Order Theory of (ω 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. The present paper is partly based on [?] Dagstuhl Seminar Proceedings 07441 Algorithmic-Logical Theory of Infinite Structures
doi:10.1007/11944836_27 fatcat:lhvcjbdb5ndyroma2moiollgfa