CL.BOYER@UTEXAS-20.ARPA (03/08/84)
From: Bob Boyer <CL.BOYER@UTEXAS-20.ARPA>
[Forwarded from the UTexas-20 bboard by Laws@SRI-AI.]
A. P. Morse, Professor of Mathematics at UC Berkeley, author
of the book "A Theory of Sets," died on Monday, March 5.
Morse's formal theory of sets, sometimes called Kelley-Morse
set theory, is perhaps the most widely used formal theory
ever developed. Morse and his students happily wrote proofs
of serious mathematical theorems (especially in analysis)
within the formal theory; it is rare for formal theories
actually to be used, even by their authors. A key to the
utility of Morse's theory of sets is a comprehensive
definitional principle, which permits the introduction of
new concepts, including those that involve indicial (bound)
variables. Morse's set theory was the culmination of the
von Neumann, Bernays, Godel theory of sets, a theory that
discusses sets (or classes) so "large" that they are not
members of any set. Morse took delight in making the
elementary elegant. His notion of ordered pair "works" even
if the objects being paired are too "big" to be members of a
set, something not true about the usual notion of ordered
pairs. Morse's theory of sets identifies sets with
propositions, conjunction with intersection, disjunction
with union, and so forth. Through his students (e.g., W. W.
Bledsoe), Morse's work has influenced automatic
theorem-proving. This influence has shaped the development
of mechanized logics and resulted in mechanical proofs of
theorems in analysis and other nontrivial parts of
mathematics.