We give a new simple proof of the decidability of the First Order Theory of \(({\omega}^{{\omega}^i},+)\) 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.


Decision Procedure Order Theory Atomic Proposition Limit Transition Tree Automaton 
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© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Thierry Cachat
    • 1
  1. 1.LIAFACNRS UMR 7089 & Université Paris 7France

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