  A universal schema for diagonalization was popularized by N. S. Yanofsky
(2003) in which the existence of a (diagonolized-out and contradictory) object
implies the existence of a fixed-point for a certain function. It was shown
that many self-referential paradoxes and diagonally proved theorems can fit in
that schema. Here, we fit more theorems in the universal schema of
diagonalization, such as Euclid's theorem on the infinitude of the primes and
new proofs of Boolos (1997) for Cantor's theorem on the non-equinumerosity of a
set with its powerset. Then, in Linear Temporal Logic, we show the
non-existence of a fixed-point in this logic whose proof resembles the argument
of Yablo's paradox. Thus, Yablo's paradox turns for the first time into a
genuine mathematico-logical theorem in the framework of Linear Temporal Logic.
Again the diagonal schema of the paper is used in this proof, and also it is
shown that G. Priest's inclosure schema (1997) can fit in our universal
diagonal/fixed-point schema. We also show the existence of dominating
(Ackermann-like) functions (which dominate a given countable set of
functions---like primitive recursives) using the schema.
