Mathematics and Applied Mathematics
October 19, 2021
Actual infinity, potential infinity, supertask, undecidable sets, undecidable sentence, self-reference, Gödel theorem.
This paper makes use of supertask theory to test the undecidable nature of computationally undecidable sets and of Gödel's undecidable sentence involved in Gödel's First Incompleteness Theorem. By means of supertasks, this Part 1 proves that computationally undecidable sets should be decidable, and that the self-reference of Gödel's sentence could be inconsistent (Part 2 proves it is). Since supertasks are legitimated by the Axiom of Infinity, either this axiom is inconsistent or the arguments proving the undecidable nature of computationally undecidable sets and Gödel's undecidable sentence are somehow wrong.