Edward Nelson (May 4, 1932 – September 10, 2014) was a professor in the Mathematics Department at Princeton University.
Nelson argued for a position in the philosophy of mathematics known as ultrafinitism:
Nelson 2011 also defined a first-order theory that was weaker than Peano arithmetic, which replaces the induction schema of induction on natural numbers with a predicate and two axioms that state that induction on natural numbers for that predicate is true.
He did not give a name to the theory, so it has been called “Nelson arithmetic” for lack of a better name.
At one point Nelson claimed to have a formal proof of inconsistency of Peano arithmetic (PA). While the proof was ultimately acknowledged by Nelson to be wrong, given that the suspicion that PA might be inconsistent after all is shared by others (e.g. Vladimir Voevodsky), it is still interesting to see Nelson’s proof strategy via Chaitin's incompleteness theorem:
Edward Nelson, Outline (of an attempt to prove inconsistency of PA) (~2011) [pdf, pdf]
Edward Nelson, Elements, 2015 [arXiv:1510.00369 [math.LO]]
Last revised on November 13, 2023 at 00:17:06. See the history of this page for a list of all contributions to it.