FOM: Math Reviews classification
Andreas Blass
ablass at math.lsa.umich.edu
Mon Jul 20 18:47:51 EDT 1998
I strongly encouraged Mathematical Reviews to drop the 04
classification for set theory and to use only 03E. Since some
questions have arisen about the appropriateness of this change, I
should explain why I favored it.
The topics listed in 04 are almost entirely duplicates of
topics in 03E, so it is difficult to say which items should get which
classification. At one time, I was told by an editor of Math Reviews
that the criterion was whether the work was metamathematical (03E) or
not (04); consistency and independence results were the primary
examples of metamathematical set theory. This criterion is
practically inapplicable to most of current set theory; consistency
results are inextricably mixed with purely combinatorial arguments.
The situation was also influenced by the Omega Bibliography of
Mathematical Logic, which used a classification system based on the
Math Reviews system, or more precisely on the 03 part of the MR
system. The Omega Bibliography saved large quantities of paper and
ink by not printing "03" everywhere, but this required inventing new
categories within 03 for topics that MR put into 04, 08, 68, and
perhaps other categories. As a result, 03E was built into a good
general classification system for set theory, while 04 was somewhat
neglected.
Perhaps because of this, perhaps because most contemporary set
theory has at least some metamathematical aspects, and perhaps because
of people (like me) who put 03E rather than 04 classifications on
their own papers and on papers they reviewed, most of set theory came
to be classified in 03E. Recently, 04 has been largely filled with
fuzzy set theory and related topics. (In the first 5 MR issues for
1998, approximately two thirds of the reviews in 04 pertain to fuzzy
things --- sometimes not even sets.) My impression is that the few
"regular" papers in 04 are somewhat lost amid the fuzz. Under these
circumstances, it did not seem worthwhile to keep 04 as a separate
classification.
Let me emphasize that merging 04 into 03E is not intended (by
me or by the MR editors) to say that set theory is not a subject in
its own right or that its only (or even primary) value is
foundational. Model theory, for example, has lived entirely in 03 for
as long as 03 has existed; yet I believe that contemporary model
theory is at least as autonomous a subject as set theory and that
most of it has little to do with foundations. Recursion theory also
has grown far beyond its foundational roots, but it has always been in
03.
Andreas Blass
P.S. For many years the inside back cover of the American Journal of
Mathematics contained, in the instructions for authors, a sample
bibliograpic entry, "Zur Theorie des Untermengenraumes der abstrakten
Leermenge (Bulletin de la Societe Philharmonique de Zanzibar)." This
practice ceased in 1982. I'd like to think it ceased because
of increased respect for set theory, but I suppose the real reason is
simply that the joke had gotten too old.
---------------------------------------------
Andreas Blass
Professor of Mathematics
University of Michigan
Interests: Logic, set theory, categories, combinatorics, and some
parts of computer science
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