Comparing Inductive and Circular Definitions: Parameters, Complexity and Games

Gupta-Belnap-style circular definitions use all real numbers as possible starting points of revision sequences. In that sense they are boldface definitions. We discuss lightface versions of circular definitions and boldface versions of inductive definitions. 2000 Mathematics Subject Classification: 03B99 03D99 03A05 91A80 03D70 03E47 03E60 03B80 ∗ The second author would like to thank the Institut für Logik und Grundlagenforschung at the Westfälische Wilhelms-Universität Münster for their hospitality during Winter Term 2001/2002. Furthermore, he’d like to extend his gratitude for a DFG Travel Grant (KON 88/2002–LO 834/3–1) to the 2002 ASL Spring Meeting in Seattle WA. † The paper was partially written while the third author was funded by DFG Grant KO 1353/2-1. ‡ The fourth author wishes to thank the Rheinische Friedrich-WilhelmsUniversität Bonn and the DFG for a Mercator-Gastprofessur held in Bonn during 2002 and 2003. He wishes to acknowledge further support from the British Academy for the project Logical Methods in Epistemology, Semantics, & Philosophy of Mathematics.