The paper with title Beyond Undecidable
definitely that Gödel's incompleteness argumentation
is not a theorem. The proof has many consequences but
the main one is the solution of the Entscheidungsproblem.
The paper with title Beyond Uncountable proves, immediately by the axioms of ZF, that Cantor's argumentation for reaching more-than-denumerable sets is not a theorem.Results here presented are not so shocking, and can be better comprehended, considering that: a) each proof of undecidability is based on diagonalization, in the literature there is no proof of undecidability without an underlying diagonalization, b) in spite of the widespread belief by which "diagonalization is only a contradiction",   diagonalization leads to a contradiction   but "  not only ", as showed by both papers, the acceptance of diagonalization as method of proof, leads immediately to the inconsistency of the theory (PA, as proved in   Beyond Undecidable , ZF, as proved in   Beyond Uncountable). Briefly, diagonalization is a way to insert a contradiction into the theory mistaking it for a proof.
In both papers the definition of the complement of the object of diagonalization brings to light the fact that diagonalization mistakes a contradiction for a proof. All that claims for something missing at the level of the theory of definition. Along this way the inquiry yielded recently a treatment for Russell's antinomy, exposed in   For a new Comprehension.
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