__Journal article:__

** Samuel R. Buss, Alexander A. Kechris, Anand Pillay, Richard
A. Shore.
"Prospects for mathematical logic in the twenty-first
century."
Journal of Symbolic Logic 7 (2001) 169-196.**

** Download postscript or PDF.**

** Abstract: **The four authors present their
speculations about the future developments of mathematical logic in the twenty-first
century. The areas of recursion theory, proof theory and logic for computer science, model
theory, and set theory are discussed independently.

**From the introduction: **The annual meeting of the
Association for Symbolic Logic held in Urbana-Champaign, June 2000, included a panel
discussion on ``The Prospects for Mathematical Logic in the Twenty-First Century''.
The panel discussions included independent presentations by the four panel members,
followed by approximately one hour of lively discussion with members of the audience.

The main themes of the discussions concerned the directions
mathematical logic should or could pursue in the future. Some members of the audience
strongly felt that logic needs to find more applications to mathematics; however, there
was disagreement as to what kinds of applications were most likely to be possible and
important. Many people also felt that applications to computer science will be of great
importance. On the other hand, quite a few people, while acknowledging the importance of
applications of logic, felt that the most important progress in logic comes from internal
developments.

It seems safe to presume that the future of mathematical logic will
include a multitude of directions and a blend of these various elements. Indeed, it speaks
well for the strength of the field that there are multiple compelling directions for
future progress. It is to be hoped that logic will be driven both by internal developments
and by external applications, and that these different directions will complement and
strengthen each other.

The present article consists of reports by the four panel members, at
times expanding on their panel presentations. As in the panel discussion, the
presentations are divided into four subareas of logic. The topics are ordered as in the
panel discussion: R.~Shore discusses recursion theory in section~2; S.~Buss discusses
proof theory and computer science logic in section~3; A.~Pillay discusses model theory in
section~4; and A.~Kechris discusses set theory in section~5.

** Download postscript or PDF.**