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 | |||||||||
| Keywords | No keywords specified (fix it) | |||||||||
| Categories | ||||||||||
| Options |
|
|||||||||
Download options| PhilPapers Archive |
Upload a copy of this paper Check publisher's policy on self-archival Papers currently archived: 5,705 |
| External links |
  Try with proxy. |
| Through your library | Configure |
Similar books and articlesAntonio Montalbán (2011). Open Questions in Reverse Mathematics. Bulletin of Symbolic Logic 17 (3):431-454.
I. Loeb (2012). Questioning Constructive Reverse Mathematics. Constructivist Foundations 7 (2):131-140.
H. Jerome Keisler (2006). Nonstandard Arithmetic and Reverse Mathematics. Bulletin of Symbolic Logic 12 (1):100-125.
Takeshi Yamazaki (2001). Reverse Mathematics and Completeness Theorems for Intuitionistic Logic. Notre Dame Journal of Formal Logic 42 (3):143-148.
Jared R. Corduan & François G. Dorais (2012). On the Indecomposability of $\Omega^{N}$. Notre Dame Journal of Formal Logic 53 (3):373-395.
Andrew Arana (2010). Proof Theory in Philosophy of Mathematics. Philosophy Compass 5 (4):336-347.
Carl Mummert (2006). Reverse Mathematics of Mf Spaces. Journal of Mathematical Logic 6 (02):203-232.
Alexander P. Kreuzer (2012). Non-Principal Ultrafilters, Program Extraction and Higher-Order Reverse Mathematics. Journal of Mathematical Logic 12 (01):1250002-.
Jeffry L. Hirst & Carl Mummert (2010). Reverse Mathematics and Uniformity in Proofs Without Excluded Middle. Notre Dame Journal of Formal Logic 52 (2):149-162.
Stewart Shapiro (1991). Foundations Without Foundationalism: A Case for Second-Order Logic. Oxford University Press.
Reed Solomon (1999). Ordered Groups: A Case Study in Reverse Mathematics. Bulletin of Symbolic Logic 5 (1):45-58.
Analytics
Monthly downloads |
Added to index2010-10-06Total downloads17 ( #71,160 of 549,224 )Recent downloads (6 months)1 ( #63,397 of 549,224 )How can I increase my downloads? |
My notes
Discussion
