An Ubiquitous Fixed Point Calculation

Abstract

It was around 1976 that David Guaspari introduced the witness comparison notation. The importance of this has already been indicated by the results of Chapter 6: It provided just the right framework for a discussion of Rosser sentences. Rosser introduced the use of witness comparisons in 1936 and, from then until Guaspari introduced his notation, most applications of self-reference in arithmetic used the comparison in a surprisingly uniform manner; yet the users neither recognised the uniformity nor attempted to explain their use of self-reference other than to make a passing reference to “Rosser’s trick.” But when the new notation came on the scene, the uniformity was readily apparent (modulo a little standardisation).