[1]Bianchini, Caterina and Sorbi, Andrea, A note on closed degrees of difficulty of the Medvedev lattice, Mathematical Logic Quarterly, vol. 42 (1996), no. 1, pp. 127–133.

[2]Dyment, Elena Z., Certain properties of the Medvedev lattice, Mathematics of the USSR Sbornik, vol. 30 (1976), pp. 321–340.

[3]Dyment, Elena Z., Exact bounds ofdenumerable collections of degrees of difficulty, Matematicheskie Zametki, vol. 28 (1980), no. 6, pp. 899–910.

[4]Hodges, Wilfrid, A shorter model theory, Cambridge University Press, 1997.

[5]Jankov, V. A., The calculus of the weak law of excluded middle, Mathematics of the USSR-Izvestiya, vol. 2 (1968), no. 5, pp. 997–1004.

[6]Lerman, Manuel, Degrees of unsolvability, Springer-Verlag, 1983.

[7]Lewis, Andrew E. M., Nies, André, and Sorbi, Andrea, The first order theories of the Medvedev and Muchnik lattices, 5th Conference on Computability in Europe, CiE 2009 (Ambos-Spies, Klaus, Löwe, Benedikt, and Merkle, Wolfgang, editors), Lecture Notes in Computer Science, vol. 5635, Springer, 2009, pp. 324–331.

[8]Lewis, Andrew E. M., Shore, Richard A., and Sorbi, Andrea, *Topological aspects of the Medvedev lattice*, to appear.

[9]Medvedev, Yuri T., Degrees of difficulty of the mass problems, Doklady Akademii Nauk SSSR (NS), vol. 104, 1955, pp. 501–504.

[10]Medvedev, Yuri T., Finite problems, Doklady Akademii Nauk SSSR (NS), vol. 142, 1962, pp. 1015–1018.

[11]Muchnik, Albert A., On strongandweak reducibilities of algorithmic problems, Sibirskii Matematkheskii Zhurnal, vol. 4 (1963), pp. 1328–1341.

[12]Nies, André, Shore, Richard A., and Slaman, Theodore A., Interpretability and definability in the recursively enumerable degrees, Proceedings of the London Mathematical Society, vol. 77 (1998), no. 02, pp. 241–291.

[13]Shafer, Paul, Characterizing the join-irreducible Medvedev degrees, Notre Dame Journal of Formal Logic, to appear.

[14]Shore, Richard A., The theory of the degrees below 0′, Journal of the London Mathematical Society, vol. 24 (1981), pp. 1–14.

[15]Simpson, Stephen G., First-order theory of the degrees of recursive unsolvability, Annals of Mathematics, vol. 105 (1977), no. 1, pp. 121–139.

[16]Simpson, Stephen G., Subsystems of second order arithmetic, Cambridge University Press, 2009.

[17]Skvortsova, Elena Z., A faithful interpretation of the intuitionistic propositional calculus by means of an initial segment of the Medvedev lattice, Sibirskii Matematicheskii Zhurnal, vol. 29 (1988), no. 1, pp. 171–178.

[18]Soare, Robert I., Recursively enumerable sets and degrees, Springer-Verlag, 1987.

[19]Sorbi, Andrea, Some remarks on the algebraic structure of the Medvedev lattice, this Journal, vol. 55 (1990), no. 2, pp. 831–853.

[20]Sorbi, Andrea, Embedding Brouwer algebras in the Medvedev lattice, Notre Dame Journal of Formal Logic, vol. 32 (1991), no. 2, pp. 266–275.

[21]Sorbi, Andrea, Some quotient lattices of the Medvedev lattice, Zeitschrift fur Mathematische Logik und Grundlagen der Mathematik, vol. 37 (1991), no. 9–12, pp. 167–182.

[22]Sorbi, Andrea, The Medvedev lattice of degrees of difficulty, Computability, enumerability, unsolvability: Directions in recursion theory (Cooper, S. B., Slaman, T. A., and Wainer, S. S., editors), London Mathematical Society Lecture Notes, vol. 224, Cambridge University Press, 1996, pp. 289–312.

[23]Sorbi, Andrea and Terwijn, Sebastiaan A., Intermediate logics and factors of the Medvedev lattice, Annals of Pure and Applied Logic, vol. 155 (2008), no. 2, pp. 69–85.