# Rosser’s Clever Improvement to GĂ¶del’s Original First Incompleteness Theorem

Sometimes it’s the case that in a first-order system T in which you can do number theory there is a property P(n) of natural numbers such that the following two seemingly contradictory statements hold: For every n, T proves P(n) and T does not prove that for all n, P(n) To see that these statements […]