I submit, to your consideration, this paper by Frank Tipler, Professor at Tulane University. The paper was published in the peer-reviewed Reports on Progress in Physics, volume 68 (2005), pages 897-964. Tipler's book "The Physics of Christianity" is based on this paper.
Tipler invokes Gödel's theorem (see p. 905 onwards), Presburger arithmetic, Löwenheim-Skolem, Hales' proof of the Kepler conjecture (the latter only as an example, I believe), and various other mathematical results.
