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

@inproceedings{Riba2012AMT,
  title={A Model Theoretic Proof of Completeness of an Axiomatization of Monadic Second-Order Logic on Infinite Words},
  author={Colin Riba},
  booktitle={IFIP TCS},
  year={2012}
}
We discuss the completeness of an axiomatization of Monadic SecondOrder Logic (MSO) on infinite words. By using model-theoretic tools, 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-Fräıssé method for Henkin models of MSO. Our main technical contribution is an infinitary Feferman… CONTINUE READING

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