[ARI0]
Afshari, Bahareh and Rathjen, Michael, A note on the theory of positive induction,
, Archive for Mathematical Logic, vol. 49 (2010), no. 2, pp. 275–281.
[ASKHLS04]
Ambos-Spies, Klaus, Kjos-Hanssen, Bjørn, Lempp, Steffen, and Slaman, Theodore A., Comparing DNR and WWKL, The Journal of Symbolic Logic, vol. 69 (2004), no. 4, pp. 1089–1104.
[Avi09]
Avigad, Jeremy, The metamathematics of ergodic theory, Annals of Pure and Applied Logic, vol. 157 (2009), no. 2–3, pp. 64–76.
[AS06]
Avigad, Jeremy and Simic, Ksenija, Fundamental notions of analysis in subsystems of second-order arithmetic, Annals of Pure and Applied Logic, vol. 139 (2006), no. 1–3, pp. 138–184.
[Bla05]
Blass, Andreas, Some questions arising from Hindman s theorem, Scientiae Mathematicae Japonicae, vol. 62 (2005), no. 2, pp. 331–334.
[BHS87]
Blass, Andreas, Hirst, Jeffry L., and Simpson, Stephen G., Logical analysis of some theorems of combinatorics and topological dynamics, Logic and combinatorics, Contemporary Mathematics, vol. 65, American Mathematical Society, Providence, RI, 1987, pp. 125–156.
[BW]
Bovykin, A. and Weiermann, A., The strength of infinitary Ramseyan principles can be accessed by their densities,
Annals of Pure and Applied
, to appear.
[BMN]
Brattka, Vasco, Miller, Joseph, and Nies, Andre, Randomness and differentiability, in preparation.
[Bus86]
Buss, Samuel R., Bounded arithmetic, Studies in Proof Theory. Lecture Notes, vol. 3, Bibliopolis, Naples, 1986.
[Car88]
Carlson, Timothy J., Some unifying principles in Ramsey theory, Discrete Mathematics, vol. 68 (1988), no. 2-3, pp. 117–169.
[CarOl]
Carlson, Timothy J., Elementary patterns of resemblance, Proceedings of the XIth Latin American Symposium on Mathematical Logic (Mérida, 1998), vol. 108, 2001, pp. 19–77.
[Car09]
Carlson, Timothy J., Patterns of resemblance of order 2, Annals of Pure and Applied Logic, vol. 158 (2009), no. 1-2, pp. 90–124.
[CS84]
Carlson, Timothy J. and Simpson, Stephen G., A dual form of Ramsey's theorem, Advances in Mathematics, vol. 53 (1984), pp. 265–290.
[CGHJ05]
Cholak, Peter A., Giusto, Mariagnese, Hirst, Jeffry L., and Jockusch, Carl G., Free sets and reverse mathematics, Reverse mathematics 2001 (Simpson, Stephen G., editor), Lecture Notes in Logic, vol. 21, Association for Symbolic Logic, La Jolla, CA, 2005, pp. 104–119.
[CJS01]
Cholak, Peter A., Jockusch, Carl G., and Slaman, Theodore A., On the strength of Ramsey's theorem for pairs, The Journal of Symbolic Logic, vol. 66 (2001), no. 1, pp. 1–55.
[CJS09]
Cholak, Peter A., Corrigendum to: On the strength of Ramsey’s theorem for pairs, The Journal of Symbolic Logic, vol. 74 (2009), no. 4, pp. 1438–1439.
[CMS04]
Cholak, Peter A., Marcone, Alberto, and Solomon, Reed, Reverse mathematics and the equivalence of definitions for well and better quasi-orders, The Journal of Symbolic Logic, vol. 69 (2004), no. 3, pp. 683–712.
[CLY10]
Chong, C. T., Lempp, Steffen, and Yang, Yue, On the role of the collection principle for -formulas in second-order reverse mathematics, Proceedings of the American Mathematical Society, vol. 138 (2010), no. 3, pp. 1093–1100.
[CHM09]
Chubb, Jennifer, Hirst, Jeffry L., and Mcnicholl, Timothy H., Reverse mathematics, computability, and partitions of trees, The Journal of Symbolic Logic, vol. 74 (2009), no. 1, pp. 201–215.
[Con10]
Conidis, C. J., Chain conditions in computable rings, Transactions of the American Mathematical Society, vol. 362 (2010), no. 12, pp. 6523–6550.
[Con]
Conidis, C. J., The strength of the Bolzano-Weierstrass theorem, submitted for publication.
[CGM]
Corduan, J., Groszek, M., and Mileti, J., A note on reverse mathematics and partitions of trees, submitted for publication.
[dJP77]
de Jongh, D. H. J. and Parikh, Rohit, Well-partial orderings and hierarchies, Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen Series A. Indagationes Mathematicae, vol. 39 (1977), no. 3 [80], pp. 195–207.
[DHLS03]
Downey, Rodney G., Hirschfeldt, Denis R., Lempp, Steffen, and Solomon, Reed, Computability-theoretic and proof-theoretic aspects of partial and linear orderings, Israel Journal of Mathematics, vol. 138 (2003), pp. 271–352.
[DH09]
Dzhafarov, Damir D. and Hirst, Jeffry L., The polarized Ramsey's theorem, Archive for Mathematical Logic, vol. 48 (2009), no. 2, pp. 141–157.
[DLH10]
Dzhafarov, Damir D., Lakins, T. J., and Hirst, J. L., Ramsey's theorem for trees: the polarized tree theorem and notions of stability, Archive for Mathematical Logic, vol. 49 (2010), no. 3, pp. 399–415.
[EM64]
Erdős, P. and Moser, L., On the representation of directed graphs as unions of orderings, Magyar Tud. Akad. Mat. Kutató Int. Közl., vol. 9 (1964), pp. 125–132.
[FF02]
Fernandes, António M. and Ferreira, Fernando, Groundwork for weak analysis, The Journal of Symbolic Logic, vol. 67 (2002), no. 2, pp. 557–578.
[Fra48]
Fraïssé, Roland, Sur la comparaison des types d'ordres, Comptes rendus de l'Académie des sciences de Paris, vol. 226 (1948), pp. 1330–1331.
[Fri75]
Friedman, Harvey, Some systems of second order arithmetic and their use, Proceedings of the International Congress of Mathematicians (Vancouver, B. C., 1974), vol. 1, Canadian Mathematics Congress, Montreal, Quebec, 1975, pp. 235–242.
[Fri09]
Friedman, Harvey, The inevitability of logical strength: strict reverse mathematics, Logic Colloquium 2006 (Cooper, Barry, Geuvers, Herman, Pillay, Anand, and Väänänen, Jouko, editors), Lecture Notes in Logic, vol. 32, Association for Symbolic Logic, Chicago, IL, 2009, pp. 135–183.
[Fri]
Friedman, Harvey, Metamathematics of ulm theory, manuscpript dated November
2001.
[FMW]
Friedman, Harvey, Montalbán, Antonio, and Weiermann, Andreas, A characterization of ATR_{0} in terms of a Kruskal-like tree theorem, unpublished draft.
[FS00]
Friedman, Harvey and Simpson, Stephen G., Issues and problems in reverse mathematics, Computability theory and its applications (Boulder, CO, 1999), Contemporary Mathematics, vol. 257, American Mathematical Society, Providence, RI, 2000, pp. 127–144.
[FSS83]
Friedman, Harvey, Simpson, Stephen G., and Smith, Rick L., Countable algebra and set existence axioms, Annals of Pure and Applied Logic, vol. 25 (1983), no. 2, pp. 141–181.
[GHR10]
Gács, Peter, Hoyrup, Mathieu, and Rojas, Cristóbal, Randomness on computable probability spaces—a dynamical point of view, Theory of Computing Systems, special issue STACS 09, 2010.
[Gir81]
Girard, Jean-Yves,
-logic. I. Dilators, Annals of Mathematical Logic, vol. 21 (1981), no. 2-3, pp. 75–219.
[Gir87]
Girard, Jean-Yves, Proof theory and logical complexity, Bibliopolis, Naples, 1987.
[GM98]
Giusto, Mariagnese and Marcone, Alberto, Lebesgue numbers and A tsuji spaces in subsystems of second-order arithmetic, Archive for Mathematical Logic, vol. 37 (1998), no. 5-6, pp. 343–362.
[GS00]
Giusto, Mariagnese and Simpson, Stephen G., Located sets and reverse mathematics, The Journal of Symbolic Logic, vol. 65 (2000), no. 3, pp. 1451–1480.
[GM08]
Greenberg, N. and Montalbán, A., Ranked structures and arithmetic transfinite recursion, Transactions of the AMS, vol. 360 (2008), pp. 1265–1307.
[HS07]
Hirschfeldt, Denis R. and Shore, Richard A., Combinatorial principles weaker than Ramsey's theorem for pairs, The Journal of Symbolic Logic, vol. 72 (2007), no. 1, pp. 171–206.
[Hir94]
Hirst, Jeffry L., Reverse mathematics and ordinal exponentiation, Annals of Pure and Applied Logic, vol. 66 (1994), no. 1, pp. 1–18.
[Hir04]
Hirst, Jeffry L., Hindman's theorem, ultrafilters, and reverse mathematics, The Journal of Symbolic Logic, vol. 69 (2004), no. 1, pp. 65–72.
[Hun08]
Hunter, James, Higher-order reverse topology, Ph.D. thesis, University of Wisconsin-Madison, 2008.
[Joc72]
Jockusch, Carl G., Ramsey's theorem and recursion theory, The Journal of Symbolic Logic, vol. 37 (1972), pp. 268–280.
[JS72]
Jockusch, Carl G. and Soare, Robert I.,
classes and degrees of theories, Transactions of the American Mathematical Society, vol. 173 (1972), pp. 33–56.
[Kap69]
Kaplansky, Irving, Infinite abelian groups, revised ed., The University of Michigan Press, Ann Arbor, Michigan, 1969.
[KP77]
Kirby, L. A. S. and Paris, J. B., Initial segments of models of Peano's axioms, Set theory and hierarchy theory, V (Proceeding of the Third Conference, Bierutowice, 1976), Lecture Notes in Mathematics, vol. 619, Springer, Berlin, 1977, pp. 211–226.
[Koh05]
Kohlenbach, Ulrich, Higher order reverse mathematics, Reverse mathematics 2001 (Simpson, Stephen G., editor), Lecture Notes in Logic, vol. 21, Association for Symbolic Logic, La Jolla, CA, 2005, pp. 281–295.
[Lav71]
Laver, Richard, On Fraïssé's order type conjecture, Annals of Mathematics (2), vol. 93 (1971), pp. 89–111.
[MW85]
Mansfield, Richard and Weitkamp, Galen, Recursive aspects of descriptive set theory, Oxford Logic Guides, vol. 11, The Clarendon Press Oxford University Press, New York, 1985, with a chapter by Stephen Simpson.
[Mar96]
Marcone, Alberto, On the logical strength of Nash–Williams' theorem on trans-finite sequences, Logic: from foundations to applications (Staffordshire, 1993), Oxford Sciene Publications, Oxford University Press, New York, 1996, pp. 327–351.
[Mar05]
Marcone, Alberto, Wqo and bqo theory in subsystems of second order arithmetic, Reverse mathematics 2001 (Simpson, Stephen G., editor), Lecture Notes in Logic, vol. 21, Association for Symbolic Logic, La Jolla, CA, 2005, pp. 303–330.
[MM]
Marcone, Alberto and Montalbán, Antonio, The Veblen functions for computability theorists, submitted for publication.
[MM09]
Marcone, Alberto, On Fraïssé’s conjecture for linear orders offinite Hausdorff rank, Annals of Pure and Applied Logic, vol. 160 (2009), pp. 355–367.
[McN95]
McNicnoll, T. H., The inclusion problem for generalized frequency classes, Ph.D. thesis, The George Washington University, 1995.
[MT07]
Medsalem, Medyahya Ould and Tanaka, Kazuyuki,
-determinacy, comprehension and induction, The Journal of Symbolic Logic, vol. 72 (2007), no. 2, pp. 452–462.
[Mil04]
Mileti, Joseph R., Partition theorems and computability theory, Ph.D. thesis, University of Illinois at Urbana-Champaign, 2004.
[MS04]
Miller, Joseph S. and Solomon, Reed, Effectiveness for infinite variable words and the dual Ramsey theorem, Archive for Mathematical Logic, vol. 43 (2004), no. 4, pp. 543–555.
[Mon]
Montalbán, Antonio, Ordinal functors and pi-1-1-ca-knot, unpublished notes dated December 7, 2009.
[Mon05]
Montalbán, Antonio, Up to equimorphism, hyperarithmetic is recursive, The Journal of Symbolic Logic, vol. 70 (2005), no. 2, pp. 360–378.
[Mon06a]
Montalbán, Antonio, Equivalence between Fraïssé's conjecture and Jullien's theorem, Annals of Pure and Applied Logic, vol. 139 (2006), no. 1-3, pp. 1–42.
[Mon06b]
Montalbán, Antonio, Indecomposable linear orderings and hyperarithmetic analysis, Journal of Mathematical Logic, vol. 6 (2006), no. 1, pp. 89–120.
[Mon07]
Montalbán, Antonio, On the equimorphism types of linear orderings, this Bulletin, vol. 13 (2007), no. 1, pp. 71-99.
[MS]
Montalbán, Antonio and Shore, Richard A., The limits of determinacy in second order arithmetic, submitted for publication.
[NW65]
Nash-Williams, C. St. J. A., On well-quasi-ordering transfinite sequences, Proceedings of the Cambridge Philosophical Society, vol. 61 (1965), pp. 33–39.
[NW68]
Nash-Williams, C. St. J. A., On better-quasi-ordering transfinite sequences, Proceedings of the Cambridge Philosophical Society, vol. 64 (1968), pp. 273–290.
[Nee]
Neeman, I., Necessary use of induction in a reversal, to appear.
[Nem09]
Nemoto, Takako, Determinacy of Wadge classes and subsystems of second order arithmetic, Mathematical Logic Quarterly, vol. 55 (2009), no. 2, pp. 154–176.
[NOMT07]
Nemoto, Takako, Medsalem, Medyahya Ould, and Tanaka, Kazuyuki, Infinite games in the Cantor space and subsystems of second order arithmetic, Mathematical Logic Quarterly, vol. 53 (2007), no. 3, pp. 226–236.
[Pat09]
Pathak, Noopur, A computational aspect of the Lebesgue differentiation theorem, Journal of Logic and Analysis, vol. 1 (2009), pp. 1–15, Paper 9.
[Rat]
Rathjen, Michael, ω-models and well-ordering principles, to appear.
[RW93]
Rathjen, Michael and Weiermann, Andreas, Proof-theoretic investigations on Kruskal's theorem, Annals of Pure and Applied Logic, vol. 60 (1993), no. 1, pp. 49–88.
[RW]
Rathjen, Michael, Reverse mathematics and well-ordering principles, Computability in context: Computation and logic in the real world
, to appear.
[Ros84]
Rosenstein, Joseph G., Recursive linear orderings, Orders: description and roles (L'Arbresle, 1982), North-Holland Mathematics Studies, vol. 99, North-Holland, Amsterdam, 1984, pp. 465–475.
[SY04]
Sakamoto, Nobuyuki and Yamazaki, Takeshi, Uniform versions of some axioms of second order arithmetic, Mathematical Logic Quarterly, vol. 50 (2004), no. 6, pp. 587–593.
[Sch79]
Schmidt, Diana, Well-partial orderings and their maximal order types, Habilitationsschrift, University of Heidelberg, 1979.
[Sh093]
Shore, Richard A., On the strength of Fraïssë's conjecture, Logical methods (Ithaca, NY, 1992), Progress in Computer Science and Applied Logic, vol. 12, Birkhäuser Boston, Boston, MA, 1993, pp. 782–813.
[SholO]
Shore, Richard A., Reverse mathematics: The playground of logic, this Bulletin, vol. 16 (2010), no. 3, pp. 378–402.
[Sho]
Shore, Richard A., Reverse mathematics, countable and uncountable: A computational approach, to appear.
[Sim09]
Simpson, Stephen G., Subsystems of second order arithmetic, second ed., Perspectives in Logic, Cambridge University Press, Cambridge, 2009.
[Sim 10]
Simpson, Stephen G., The Gödei hierarchy and reverse mathematics, Kurt Gödel: essays for his centennial (Feferman, Solomon, Parsons, Charles, and Simpson, Steven G., editors), Lecture Notes in Logic, vol. 33, Association for Symbolic Logic, La Jolla, CA, 2010, pp. 109–127.
[SS86]
Simpson, Stephen G. and Smith, Rick L., Factorization of polynomials and induction, Annals of Pure and Applied Logic, vol. 31 (1986), no. 2-3, pp. 289–306, Special issue: Second Southeast Asian logic conference (Bangkok, 1984).
[Sla]
Slaman, T. A., A note on dual Ramsey theorem, unpublished note dated January 1997.
[Sm085]
Smoryński, C., Nonstandard models and related developments, Harvey Friedman’s research on the foundations of mathematics, Studies in Logic and the Foundations of Mathematics, vol. 117, North-Holland, Amsterdam, 1985, pp. 179–229.
[Wel]
Welch, Philip, Weak systems of determinacy and arithmetical quasi-inductive definitions, submitted for publication.
[Wil06]
Wilken, Gunnar, The Bachmann-Howard structure in terms of Σ_{1}-elementarity, Archive for Mathematical Logic, vol. 45 (2006), no. 7, pp. 807–829.
[WÌ107]
Wilken, Gunnar, Assignment of ordinals to patterns of resemblance, The Journal of Symbolic Logic, vol. 72 (2007), no. 2, pp. 704–720.
[YS90]
Yu, Xiaokang and Simpson, Stephen G., Measure theory and weak Königs lemma, Archive for Mathematical Logic, vol. 30 (1990), no. 3, pp. 171–180.