One result which provides a natural example of this theorem is that certain sequences of numbers in base hereditary notation always eventually go to zero.
One result which provides a natural example of this theorem is that certain sequences of numbers in base hereditary notation always eventually go to zero. That example of this theorem was found by Paris and Harrington and was first proven by Goodstein. John Rosser strengthened this result by formulating a proof without assuming either omega-consistency or 1-consistency. Proofs of this theorem may rely on schemes such as one which maps symbols to integers and uses those integers as exponents for prime numbers. It's not Tarski's theorem, but thediagonalization lemma is used to show that one of this theorem's namesake sentences must exist. This theorem is often grouped with the result that sufficiently strong systems cannot prove their own consistency. For 10 points, name this result which states that certain theories will always contain results which are true but not provable in the theory.
One result which provides a natural example of this theorem is that certain sequences of numbers in base hereditary notation always eventually go to zero.
God el's  In comp let en ess  Theorems [accept  God el's  f irst In comp let en ess  Theorem; prompt on incompleteness theorem or Godel's theorem]