Open Questions in Reverse Mathematics

We present a list of open questions in reverse mathematics, including some relevant background information for each question. We also mention some of the areas of reverse mathematics that are starting to be developed and where interesting open question may be found.

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[26]  Stephen G. Simpson,et al.  Located sets and reverse mathematics , 2000, Journal of Symbolic Logic.

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[40]  Philip D. Welch.  Weak systems of determinacy and arithmetical quasi-inductive definitions , 2011, J. Symb. Log..

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[43]  Stephen G. Simpson,et al.  The Godel Hierarchy and Reverse Mathematics , 2008 .

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[49]  Richard A. Shore,et al.  On the strength of Fraïssé’s conjecture , 1993 .

[50]  James Hunter,et al.  HIGHER-ORDER REVERSE TOPOLOGY , 2008 .

[51]  Péter Gács,et al.  Randomness on Computable Probability Spaces—A Dynamical Point of View , 2009, Theory of Computing Systems.

[52]  Steffen Lempp,et al.  On the role of the collection principle for Sigma^0_2-formulas in second-order reverse mathematics , 2010 .

[53]  Stephen G. Simpson,et al.  Factorization of polynomials and Σ10 induction , 1986, Ann. Pure Appl. Log..

[54]  Jeffry L. Hirst.  Reverse Mathematics and Ordinal Exponentiation , 1994, Ann. Pure Appl. Log..

[55]  Fernando Ferreira,et al.  Groundwork for weak analysis , 2002, Journal of Symbolic Logic.

[56]  Alberto Marcone,et al.  Reverse mathematics and the equivalence of definitions for well and better quasi-orders , 2004, J. Symb. Log..

[57]  Marcia J. Groszek,et al.  Reverse mathematics and Ramsey's property for trees , 2010, J. Symb. Log..

[58]  Xiaokang Yu,et al.  Measure theory and weak König's lemma , 1990, Arch. Math. Log..

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[60]  Takeshi Yamazaki,et al.  Uniform versions of some axioms of second order arithmetic , 2004, Math. Log. Q..

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[62]  Jeremy Avigad,et al.  Fundamental notions of analysis in subsystems of second-order arithmetic , 2006, Ann. Pure Appl. Log..

[63]  Jeremy Avigad,et al.  The metamathematics of ergodic theory , 2009, Ann. Pure Appl. Log..

[64]  Alberto Marcone.  On the logical strength of Nash-Williams' theorem on transfinite sequences , 1994, math/9408204.

[65]  Antonio Montalbán.  Indecomposable linear Orderings and Hyperarithmetic Analysis , 2006, J. Math. Log..

[66]  Steffen Lempp,et al.  Comparing DNR and WWKL , 2004, J. Symb. Log..

[67]  Timothy J. Carlson,et al.  Elementary patterns of resemblance , 2001, Ann. Pure Appl. Log..

[68]  Itay Neeman.  Necessary use of Σ¹₁ induction in a reversal , 2011, J. Symb. Log..

[69]  Stephen G. Simpson,et al.  A Dual Form of Ramsey's Theorem , 1984 .

[70]  Antonio Montalbán,et al.  On the Equimorphism Types of Linear Orderings , 2007, Bulletin of Symbolic Logic.

[71]  Denis R. Hirschfeldt,et al.  Combinatorial principles weaker than Ramsey's Theorem for pairs , 2007, J. Symb. Log..

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[73]  S. G. Simpson,et al.  Issues and problems in reverse mathematics , 2000 .

[74]  Richard A. Shore.  Reverse mathematics: the playground of logic , 2010, Bull. Symb. Log..

[75]  Kazuyuki Tanaka,et al.  Infinite games in the Cantor space and subsystems of second order arithmetic , 2007, Math. Log. Q..

[76]  Jeffry L. Hirst,et al.  The polarized Ramsey’s theorem , 2009, Arch. Math. Log..

[77]  Harvey M. Friedman,et al.  Logic Colloquium 2006: The inevitability of logical strength: Strict reverse mathematics , 2009 .

[78]  Alberto Marcone,et al.  Lebesgue numbers and Atsuji spaces in subsystems of second-order arithmetic , 1998, Arch. Math. Log..

[79]  Stephen G. Simpson,et al.  Countable algebra and set existence axioms , 1983, Ann. Pure Appl. Log..

[80]  Thierry Coquand,et al.  Integrals and valuations , 2008, J. Log. Anal..

[81]  Antonio Montalbán,et al.  Equivalence between Fraïssé's conjecture and Jullien's theorem , 2006, Ann. Pure Appl. Log..

[82]  ITAY NEEMAN.  NECESSARY USE OF Σ1 INDUCTION IN A REVERSAL , 2009 .

[83]  C. Chong,et al.  ON THE ROLE OF THE COLLECTION PRINCIPLE FOR Σ2-FORMULAS IN SECOND-ORDER REVERSE MATHEMATICS , 2009 .