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Issues and problems in reverse mathematics. (English) Zbl 0967.03050

Cholak, Peter A. (ed.) et al., Computability theory and its applications. Current trends and open problems. Proceedings of a 1999 AMS-IMS-SIAM joint summer research conference, Boulder, CO, USA, June 13-17, 1999. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 257, 127-144 (2000).
In this article, the founders of the program of reverse mathematics describe the history and significance of the program and their vision for its future. In addition to a substantial bibliography, they include descriptions of many tantalizing open problems in the logical analysis of theorems of topology, analysis, combinatorics, WQO theory, and countable Abelian groups. For more on reverse mathematics, see S. Simpson [Subsystems of second order arithmetic, Perspectives in Mathematical Logic. Berlin: Springer (1999; Zbl 0909.03048)].
For the entire collection see [Zbl 0945.00017].

MSC:

03F35 Second- and higher-order arithmetic and fragments
03-02 Research exposition (monographs, survey articles) pertaining to mathematical logic and foundations
06C99 Modular lattices, complemented lattices
26E40 Constructive real analysis
46B99 Normed linear spaces and Banach spaces; Banach lattices
03B30 Foundations of classical theories (including reverse mathematics)
05C55 Generalized Ramsey theory

Citations:

Zbl 0909.03048
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