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Model theoretic tools for deciding boundedness of fixed points

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Boundedness concerns the question whether a given monotone/positive first-order inductive definition converges to its fixed point within a uniformly bounded number of steps. This is equivalent to the question whether the fixed point is itself first-order, by a classical theorem of Barwise and Moschovakis. The corresponding decision problem is undecidable for all but very limited fragments of first-order logic. I want to focus on the decidability frontier for monadic fixed points and to discuss some old and new results and techniques that suggest to look for a model theoretic divide between decidable and undecidable cases.

This talk is part of the Logic and Semantics Seminar (Computer Laboratory) series.

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