Fixed point logics

Bulletin of Symbolic Logic 8 (1):65-88 (2002)
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We consider fixed point logics, i.e., extensions of first order predicate logic with operators defining fixed points. A number of such operators, generalizing inductive definitions, have been studied in the context of finite model theory, including nondeterministic and alternating operators. We review results established in finite model theory, and also consider the expressive power of the resulting logics on infinite structures. In particular, we establish the relationship between inflationary and nondeterministic fixed point logics and second order logic, and we consider questions related to the determinacy of games associated with alternating fixed points



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Citations of this work

ŁΠ logic with fixed points.Luca Spada - 2008 - Archive for Mathematical Logic 47 (7-8):741-763.
Expressive equivalence of least and inflationary fixed-point logic.Stephan Kreutzer - 2004 - Annals of Pure and Applied Logic 130 (1-3):61-78.
Symbioses between mathematical logic and computer science.Andreas Blass - 2016 - Annals of Pure and Applied Logic 167 (10):868-878.

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References found in this work

Elementary Induction on Abstract Structures.Wayne Richter - 1979 - Journal of Symbolic Logic 44 (1):124-125.
Fixed-point extensions of first-order logic.Yuri Gurevich & Saharon Shelah - 1986 - Annals of Pure and Applied Logic 32:265-280.
Descriptive Set Theory.Yiannis Nicholas Moschovakis - 1982 - Studia Logica 41 (4):429-430.
Finite Model Theory.Heinz-Dieter Ebbinghaus & Jörg Flum - 2001 - Studia Logica 69 (3):449-449.

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