Stage Comparison, Fixed Points, and Least Fixed Points in Kripke–Platek Environments
Gerhard Jäger · Notre Dame Journal of Formal Logic · 2022
Let T be Kripke–Platek set theory with infinity extended by the axiom (Beta) plus the schema that claims that every set-bounded Σ-definable monotone operator from the collection of all sets to Pow(a) for some set a has a fixed point. Then T proves that every such operator has a least fixed point. This result is obtained by following the proof of an analogous result for von Neumann–Bernays–Gödel set theory in an earlier work by Sato, with some minor modifications.