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

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

2008-02-20

arxiv.org/abs/0802.2862v1

Dans Proceedings of the 25th Annual Symposium on the Theoretical Aspects of Computer Science - STACS 2008, Bordeaux : France (

Computer Science

Logic in Computer Science

Scientific paper

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.

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