@article{Shore2010ReverseMT,
title={Reverse mathematics: the playground of logic},
author={Richard A. Shore},
journal={Bulletin of Symbolic Logic},
year={2010},
volume={16},
pages={378-402}
}

The general enterprise of calibrating the strength of classical mathematical theorems in terms of the axioms (typically of set existence) needed to prove them was begun by Harvey Friedman in [1971] (see also [1967]). His goals were both philosophical and foundational. What existence assumptions are really needed to develop classical mathematics and what other axioms and methods suffice to carry out standard constructions and proofs? In the [1971] paper, Friedman worked primarily in the set… CONTINUE READING