This classic paper of Alan Turing is the first work on this problem:

http://www.turingarchive.org/browse.php/b/15

For more recent works, see these papers of Solomon Feferman and Torkel Franzen:

http://www.jstor.org/stable/2964649?seq=1#page_scan_tab_contents

http://projecteuclid.org/euclid.bsl/1102022662