Postscript to Spector 1962 (1962)

Abstract This important paper [ Spector 1962] was written by Clifford Spector during his stay at the Institute for Advanced Study in 1960 1961 under a grant from the Office of Naval Research. The discussions P. Bernays and I had with Spector (see footnote 1) took place after the main result (contained in §10 of the paper) had been established already. However, it ought to be mentioned that during the time Spector first established this result he was in close contact with Kreisel. It was Spector’s express intention to give to Kreisel a good deal of credit for his work. Originally a joint publication by Spector and Kreisel was envisaged. This plan was dropped because Spector had taken over the elaboration by himself and because the version of the proof which was to be published was due to Spector. Also Spector alone, at that time, was working on an extension of the result in the direction of stricter constructivity which he hoped to include in his paper.