A model theoretic proof of completeness of an axiomatization of monadic second-order logic on infinite words

Authors:
Colin Riba
Affiliations:
ENS de Lyon, Université de Lyon, LIP, France
Venue:
TCS'12 Proceedings of the 7th IFIP TC 1/WG 202 international conference on Theoretical Computer Science
Year:
2012

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Abstract

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.