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.

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    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.

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