  Our main result, Theorem 2.5, shows the existence of a vast infinity of
subset sum problems solvable in polynomial time. The only proof we have of this
result uses the ZFC independent Jump Free Theorem of Harvey Friedman, thus
putting Theorem 2.5 in what we call ZFC limbo. The mathematics we use is
elementary and at the level of a good undergraduate course in combinatorics or
design and analysis of algorithms. The statement of the Jump Free Theorem is
also easily understood at this level (but not the proof).
