A Model Theoretic Proof of Completeness of an Axiomatization of Monadic Second-Order Logic on Infinite Words

  • Colin Riba
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7604)


We discuss a complete axiomatization of Monadic Second-Order Logic (MSO) on infinite words.By using model-theoretic methods, we give an alternative proof of D. Siefkes’ result that a fragment with full comprehension and induction of second-order Peano’s arithmetic is complete w.r.t the validity of MSO-formulas on infinite words. We rely on Feferman-Vaught Theorems and the Ehrenfeucht-Fraïssé method for Henkin models of MSO. Our main technical contribution is an infinitary Feferman-Vaught Fusion of such models. We show it using Ramseyan factorizations similar to those for standard infinite words.


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© IFIP International Federation for Information Processing 2012

Authors and Affiliations

  • Colin Riba
    • 1
  1. 1.ENS de Lyon, Université de Lyon, LIPFrance

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