Compatibility of Shelah and Stupp's and Muchnik's iteration with fragments of monadic second order logic

Dietrich Kuske (1)

1 Institut für Informatik [Leipzig]

We investigate the relation between the theory of the iterations in the sense of Shelah-Stupp and of Muchnik, resp., and the theory of the base structure for several logics. These logics are obtained from the restriction of set quantification in monadic second order logic to certain subsets like, e.g., finite sets, chains, and finite unions of chains. We show that these theories of the Shelah-Stupp iteration can be reduced to corresponding theories of the base structure. This fails for Muchnik's iteration.

Mots clés: Logic in computer science; Rabin's tree theorem

Domaines: Logique en informatique [cs.LO]

Dietrich Kuske. Compatibility of Shelah and Stupp's and Muchnik's iteration with fragments of monadic second order logic. STACS 2008, Feb 2008, Bordeaux, France. pp.467-478. ⟨hal-00232967⟩