> how to program a Turing machine to use "axioms stronger than PA" http://www.scottaaronson.com/blog/?p=2725 http://www.scottaaronson.com/blog/?p=2725 "... a

> how to program a Turing machine to use "axioms stronger than PA" http://www.scottaaronson.com/blog/?p=2725 http://www.scottaaronson.com/blog/?p=2725 "... a one-tape, two-symbol Turing machine with 7,918 states, whose behavior (when run on a blank tape) can never be proven from the usual axioms of set theory, under reasonable consistency hypotheses."