Diagonal arguments and fixed points

ýA universal schema for diagonalization was popularized by N.Sý. ýYanofsky (2003)ý, ýbased on a pioneering work of F.Wý. ýLawvere (1969)ý, ýin which the existence of a (diagonolized-out and contradictory) object implies the existence of a fixed-point for a certain functioný. ýIt was shown that many self-referential paradoxes and diagonally proved theorems can fit in that schemaý. ýHereý, ýwe fit more theorems in the universalý ýschema of diagonalizationý, ýsuch as Euclid's proof for the infinitude of the primes and new proofs of G.~Boolos (1997) for Cantor's theorem on the non-equinumerosity of a set with its powersetý. ýThený, ýin Linear Temporal Logicý, ýwe show the non-existence of a fixed-point in this logic whose proof resembles the argument of Yablo's paradox (1985ý, ý1993)ý. ýThusý, ýYablo's paradox turns for the first time into a genuine mathematico-logical theorem in the framework of Linear Temporal Logicý. ýAgain the diagonal schema of the paper is used in this proof; and it is also shown that G.~Priest's inclosure schema (1997) can fit in our universal diagonal/fixed-point schemaý. ýWe also show the existence of dominating (Ackermann-like) functions (which dominate a given countable set of functionsý, ýsuch as primitive recursive functions) in the schema.