Reverse mathematics: the playground of logic

Bulletin of Symbolic Logic 16 (3):378-402 (2010)
Abstract
This paper is essentially the author's Gödel Lecture at the ASL Logic Colloquium '09 in Sofia extended and supplemented by material from some other papers. After a brief description of traditional reverse mathematics, a computational approach to is presented. There are then discussions of some interactions between reverse mathematics and the major branches of mathematical logic in terms of the techniques they supply as well as theorems for analysis. The emphasis here is on ones that lie outside the usual main systems of reverse mathematics. While retaining the usual base theory and working still within second order arithmetic, theorems are described that range from those far below the usual systems to ones far above
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DOI 10.2178/bsl/1286284559
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The Polarized Ramsey's Theorem.Damir D. Dzhafarov & Jeffry L. Hirst - 2009 - Archive for Mathematical Logic 48 (2):141-157.
Direct and Local Definitions of the Turing Jump.Richard A. Shore - 2007 - Journal of Mathematical Logic 7 (2):229-262.
Forcing with Tagged Trees.John R. Steel - 1978 - Annals of Mathematical Logic 15 (1):55-74.

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