Harvey Friedman's conjecture on finite-solution Diophantine equations
Consider the collection of Diophantine equations over the rationals that have only finitely many rational solutions. Harvey Friedman's conjecture. This collection is not recursively enumerable. The paper uses this conjecture to obtain stronger negative computability consequences for recognizing finite rational solution sets; no resolution is supplied.
References
Primary source
Apoloniusz Tyszka, “Is there a computable upper bound on the heights of rational solutions of a Diophantine equation with a finite number of solutions?”, arXiv:1511.06689 (2017).
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