I study several kinds of generalizations of Montague’s theorem on the method of definition of a function by recursion on a well-founded relation. In particular, I extend Montague’s theorem to cover the following situations: recursion by a valuation system, non-well-founded recursion, and recursion on a dependence operator. By means of these extensions, several constructions employed in formal theories of truth and paradox can be recast as special applications of the generalized version of Montague’s theorem.
"Generalizing Montague’s Theorem on Recursive Definitions." Notre Dame J. Formal Logic 62 (3) 553 - 575, August 2021. https://doi.org/10.1215/00294527-2021-0027