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

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (2012) 7604 LNCS 310-324
DOI: 10.1007/978-3-642-33475-7_22
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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. © 2012 IFIP International Federation for Information Processing.

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Riba, C. (2012). A model theoretic proof of completeness of an axiomatization of monadic second-order logic on infinite words. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7604 LNCS, pp. 310–324). https://doi.org/10.1007/978-3-642-33475-7_22

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