Andretta, Alessandro [And03] Equivalence between Wadge and Lipschitz determinacy, Annals of Pure and Applied Logic, vol. 123 (2003), no. 1–3, pp. 163–192.CrossRefGoogle Scholar

Andretta, Alessandro [And06] More on Wadge determinacy, Annals of Pure and Applied Logic, vol. 144 (2006), no. 1–3, pp. 2–32.CrossRefGoogle Scholar

Andretta, Alessandro, [AHN07] Hjorth, Gregory, and Neeman, Itay Effective cardinals of boldface pointclasses, Journal of Mathematical Logic, vol. 7 (2007), no. 1, pp. 35–92.CrossRefGoogle Scholar

Andretta, Alessandro and Martin, Donald A. [AM03] Borel-Wadge degrees, Fundamenta Mathematicae, vol. 177 (2003), no. 2, pp. 175–192.CrossRefGoogle Scholar

Becker, Howard S. and Kechris, Alexander S. [BK96] The descriptive set theory of Polish group actions, London Mathematical Society Lecture Note Series, vol. 232, Cambridge University Press, Cambridge, 1996.CrossRefGoogle Scholar

Ditzen, Achim [Dit92] Definable equivalence relations on Polish spaces, Ph.D. thesis, California Institute of Technology, 1992.Google Scholar

Duparc, Jacques [Dup01] Wadge hierarchy and Veblen hierarchy. I. Borel sets of finite rank, The Journal of Symbolic Logic, vol. 66 (2001), no. 1, pp. 56–86.CrossRefGoogle Scholar

Duparc, Jacques [Dup03] A hierarchy of deterministic context-free ω-languages, Theoretical Computer Science, vol. 290 (2003), no. 3, pp. 1253–1300.CrossRefGoogle Scholar

Duparc, Jacques, Finkel, Olivier, and Ressayre, Jean-Pierre [DFR01] Computer science and the fine structure of Borel sets, Theoretical Computer Science, vol. 257 (2001), no. 1–2, pp. 85–105.CrossRefGoogle Scholar

Friedman, Harvey [Fri71B] Higher set theory and mathematical practice, Annals of Mathematical Logic, vol. 2 (1971), no. 3, pp. 325–357.CrossRefGoogle Scholar

Friedman, Harvey and Stanley, Lee [FS89] A Borel reducibility theory for classes of countable structures, The Journal of Symbolic Logic, vol. 54 (1989), no. 3, pp. 894–914.CrossRefGoogle Scholar

Harrington, Leo A. [Har78] Analytic determinacy and 0# , The Journal of Symbolic Logic, vol. 43 (1978), pp. 685–693.CrossRefGoogle Scholar

Harrington, Leo A., Kechris, Alexander S., and Louveau, Alain [HKL90] A Glimm–Effros dichotomy for Borel equivalence relations, Journal of the American Mathematical Society, vol. 3 (1990), pp. 902–928.CrossRefGoogle Scholar

Harrington, Leo A. and Sami, Ramez-Labib [HS79] Equivalence relations, projective and beyond, Logic Colloquium '78. Proceedings of the Colloquium held in Mons, August 24–September 1, 1978 (Boffa, Maurice, Dalen, Dirk van, and McAloon, Kenneth, editors), Studies in Logic and the Foundations of Mathematics, vol. 97, North-Holland, Amsterdam, 1979, pp. 247–264.CrossRefGoogle Scholar

Hjorth, Gregory [Hjo95] A dichotomy for the definable universe, The Journal of Symbolic Logic, vol. 60 (1995), no. 4, pp. 1199–1207.CrossRefGoogle Scholar

Hjorth, Gregory [Hjo96] Wadge degrees, Annals of Pure and Applied Logic, vol. 77 (1996), no. 1, pp. 53–74.CrossRefGoogle Scholar

Hjorth, Gregory [Hjo98] An absoluteness principle for Borel sets, The Journal of Symbolic Logic, vol. 63 (1998), no. 2, pp. 663–693.CrossRefGoogle Scholar

Hjorth, Gregory [Hjo02] Cardinalities in the projective hierarchy, The Journal of Symbolic Logic, vol. 67 (2002), no. 4, pp. 1351–1372.CrossRefGoogle Scholar

Hjorth, Gregory and Kechris, Alexander S. [HK01] Recent developments in the theory of Borel reducibility, Fundamenta Mathematicae, vol. 170 (2001), no. 1–2, pp. 21–52.CrossRefGoogle Scholar

Kechris, Alexander S. [Kec92] The structure of Borel equivalence relations in Polish spaces, Set theory of the continuum. Papers from the workshop held in Berkeley, California, October 16–20, 1989 (Judah, H., Just, W., and Woodin, H., editors), Mathematical Sciences Research Institute Publications, vol. 26, Springer, New York, 1992, pp. 89–102.Google Scholar

Kechris, Alexander S., Löwe, Benedikt, and Steel, John R. [Cabal I] Games, scales, and Suslin cardinals: the Cabal seminar, volume I, Lecture Notes in Logic, vol. 31, Cambridge University Press, 2008.CrossRefGoogle Scholar

Kechris, Alexander S., Martin, Donald A., and Moschovakis, Yiannis N. [Cabal iii] Cabal seminar 79–81, Lecture Notes in Mathematics, no. 1019, Berlin, Springer, 1983.CrossRefGoogle Scholar

Kechris, Alexander S., Martin, Donald A., and Steel, John R. [Cabal iv] Cabal seminar 81–85, Lecture Notes in Mathematics, no. 1333, Berlin, Springer, 1988.CrossRefGoogle Scholar

Kechris, Alexander S. and Moschovakis, Yiannis N. [Cabal i] Cabal seminar 76–77, Lecture Notes in Mathematics, no. 689, Berlin, Springer, 1978.CrossRefGoogle Scholar

Kechris, Alexander S. and Moschovakis, Yiannis N. [KM78B] Notes on the theory of scales, in Cabal Seminar 76–77 [Cabal i], pp. 1–53, reprinted in [Cabal I], p. 28–74.Google Scholar

Kuratowski, Casimir [Kur58] Topologie. Vol. I, 4ème ed., Matematyczne, Monografie, vol. 20, Państwowe Wydawnictwo Naukowe, Warsaw, 1958.Google Scholar

Laver, Richard [Lav71] On Fraïssé's order type conjecture, Annals of Mathematics, vol. 93 (1971), pp. 89–111.CrossRefGoogle Scholar

Louveau, Alain [Lou80] A separation theorem for sets, Transactions of the American Mathematical Society, vol. 260 (1980), no. 2, pp. 363–378.Google Scholar

Louveau, Alain [Lou83] Some results in the Wadge hierarchy of Borel sets, this volume, originally published in Kechris et al. [Cabal iii], pp. 28–55.Google Scholar

Louveau, Alain [Lou92] Classifying Borel structures, Set Theory of the Continuum. Papers from the workshop held in Berkeley, California, October 16–20, 1989 (Judah, H., Just, W., and Woodin, H., editors), Mathematical Sciences Research Institute Publications, vol. 26, Springer, New York, 1992, pp. 103–112.Google Scholar

Louveau, Alain [Lou94] On the reducibility order between Borel equivalence relations, Logic, Methodology and Philosophy of Science, IX. Proceedings of the Ninth International Congress held in Uppsala, August 7–14, 1991 (Prawitz, Dag, Skyrms, Brian, and Westerståhl, Dag, editors), Studies in Logic and the Foundations of Mathematics, vol. 134, North-Holland, Amsterdam, 1994.Google Scholar

Louveau, Alain and Saint-Raymond, Jean [LSR87] Borel classes and closed games: Wadge-type and Hurewicz-type results, Transactions of the American Mathematical Society, vol. 304 (1987), no. 2, pp. 431–467.CrossRefGoogle Scholar

Louveau, Alain and Saint-Raymond, Jean [LSR88A] Les propriétés de réduction et de norme pour les classes de Boréliens, Fundamenta Mathematicae, vol. 131 (1988), no. 3, pp. 223–243.CrossRefGoogle Scholar

Louveau, Alain and Saint-Raymond, Jean [LSR88B] The strength of Borel Wadge determinacy, this volume, originally published in Kechris et al. [Cabal iv], pp. 1–30.Google Scholar

Louveau, Alain and Saint-Raymond, Jean [LSR90] On the quasi-ordering of Borel linear orders under embeddability, The Journal of Symbolic Logic, vol. 55 (1990), no. 2, pp. 537–560.CrossRefGoogle Scholar

Luzin, Nikolai and Sierpiński, Waclaw [LS29] Sur les classes des constituantes d'un complémentaire analytique, Comptes rendus hebdomadaires des séances de l'Académie des Sciences, vol. 189 (1929), pp. 794–796.Google Scholar

Mansfield, Richard and Weitkamp, Galen [MW85] 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.Google Scholar

Martin, Donald A. [Mar75] Borel determinacy, Annals of Mathematics, vol. 102 (1975), no. 2, pp. 363–371.CrossRefGoogle Scholar

Ros, Luca Motto [MR07] General reducibilities for sets of reals, Ph.D. thesis, Politecnico di Torino, 2007.Google Scholar

Robertson, Neil and Seymour, P. D. [RS04] Graph minors. XX. Wagner's conjecture, Journal of Combinatorial Theory. Series B, vol. 92 (2004), no. 2, pp. 325–357.Google Scholar

Sierpiński, Waclaw [Sie52] General topology, Mathematical Expositions, No. 7, University of Toronto Press, Toronto, 1952, Translated by Krieger, C. Cecilia.CrossRefGoogle Scholar

Sikorski, Roman [Sik58] Some examples of Borel sets, Colloquium Mathematicum, vol. 5 (1958), pp. 170–171.CrossRefGoogle Scholar

Silver, Jack [Sil80] Counting the number of equivalence classes of Borel and coanalytic equivalence relations, Annals of Mathematical Logic, vol. 18 (1980), no. 1, pp. 1–28.CrossRefGoogle Scholar

Solovay, Robert M. [Sol78B] The independence of DC from AD, in Kechris and Moschovakis [Cabal i], pp. 171–184.Google Scholar

Steel, John R. [Ste77] Determinateness and subsystems of analysis, Ph.D. thesis, Berkeley, 1977.Google Scholar

Steel, John R. [Ste80] Analytic sets and Borel isomorphisms, Fundamenta Mathematicae, vol. 108 (1980), no. 2, pp. 83–88.CrossRefGoogle Scholar

Steel, John R. [Ste81B] Determinateness and the separation property, The Journal of Symbolic Logic, vol. 46 (1981), no. 1, pp. 41–44.CrossRefGoogle Scholar

Engelen, Fons van, Miller, Arnold W., and Steel, John R. [vEMS87] Rigid Borel sets and better quasi-order theory, Proceedings of the AMS-IMS-SIAM joint summer research conference on applications of mathematical logic to finite combinatorics held at Humboldt State University, Arcata, Calif., August 4–10, 1985 (Simpson, Stephen G., editor), Contemporary Mathematics, vol. 65, American Mathematical Society, Providence, RI, 1987, pp. 199–222.Google Scholar

Wesep, Robert Van [Van77] Subsystems of second-order arithmetric, and descriptive set theory under the axiom of determinateness, Ph.D. thesis, University of California, Berkeley, 1977.Google Scholar

Wesep, Robert Van [Van78A] Separation principles and the axiom of determinateness, The Journal of Symbolic Logic, vol. 43 (1978), no. 1, pp. 77–81.CrossRefGoogle Scholar

Wadge, William W. [Wad84] Reducibility and determinateness on the Baire space, Ph.D. thesis, University of California, Berkeley, 1984.Google Scholar

Wadge, William W. [Wad11] Early investigations of the degrees of Borel sets, 2011, this volume.Google Scholar

Woodin, W. Hugh [Woo99] The axiom of determinacy, forcing axioms, and the nonstationary ideal, De Gruyter Series in Logic and its Applications, Walter de Gruyter, Berlin, 1999.CrossRefGoogle Scholar