A theory of infinitary relations extending Zermelo's theory of infinitary propositions (Q284223)

By following Russell's ideas, the author extends Zermelo's theory of infinite propositions to infinitary relations. This approach enables to give an effective characterization of parametric definability with respect to a purely relational structure, as well as to highlight a new understanding of Zermelo's rejecting of Gödel's first incompleteness theorem. The theory of infinitary relations presents a suitable starting point in the reconstruction of Zermelo's original theory of urelements and sets. The status of definability and expressibility in presence of infinitary relations is deeply analyzed and determined.