[FOM] Historical notation question
hbe at math.ucla.edu
Wed Feb 25 15:33:11 EST 2004
Brian Postow was asking about the origin of the notation Sigma_i and
Pi_i for the different levels of the arithmetic hierarchy.
Panu Raatikainen ascribes it to Addison.
Certainly Addison was using this notation by the time of the 1957
Cornell meeting; see his paper from that meeting. Earlier,
I think Mostowski had been using P_i and Q_i; see his paper
in Fundamenta Mathematicae, vol. 38, pp. 81-112. Martin Davis
in this 1958 textbook followed that notation. (I hope he'll
correct me if I'm wrong here.)
I'm not sure whether the Sigma-Pi notation (which, as others have
pointed out, is quite natural) originated with Addison. I'm pretty
sure that the "lightface/boldface" distinction can be blamed on him!
(I'll cc Addison on this.)
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