[1]Beckmann, A. and Buss, S., *Polynomial local search in the polynomial hierarchy and witnessing in fragments of bounded arithmetic*, Journal of Mathematical Logic, vol. 9 (2009), pp. 103–138.

[2]Beckmann, A. and Buss, S., *Characterization of definable search problems in bounded arithmetic via proof notations*, Ways of Proof Theory, Ontos Verlag, Frankfurt 2010, pp. 65–134.

[3]Ben-Sasson, E. and Wigderson, A., *Short proofs are narrow—resolution made simple*, Journal of the ACM, vol. 48 (2001), pp. 149–169.

[4]Boughattas, S. and Kołodziejczyk, L. A., *The strength of sharply bounded induction requires MSP*, Annals of Pure and Applied Logic, vol. 161 (2010), pp. 504–510.

[5]Buss, S., Bounded Arithmetic, Bibliopolis, Napoli 1986.

[6]Buss, S., *Axiomatizations and conservation results for fragments of bounded arithmetic*, In Logic and Computation, , American Mathematical Society, 1990, pp. 57–84.

[7]Buss, S., First-order proof theory of arithmetic, In Handbook of Proof Theory (Buss, S., editor), Elsevier, Amsterdam 1998, pp. 79–147.

[8]Buss, S. and Krajíček, J., *An application of Boolean complexity to separation problems in bounded arithmetic*, Proceedings of the London Mathematical Society, vol. 69 (1994), pp. 1–21.

[9]Chiari, M. and Krajíček, J., Witnessing functions in bounded arithmetic and search problems, this Journal, vol. 63 (1998), pp. 1095–1115.

[10]Chiari, M. and Krajíček, J., *Lifting independence results in bounded arithmetic*, Archive for Mathematical Logic, vol. 38 (1999), pp. 123–138.

[11]Hájek, P. and Pudlák, P., The Metamathematics of First Order Arithmetic, Springer, Berlin 1993.

[12]Jeřábek, E., *Dual weak pigeonhole principle, Boolean complexity, and derandomization*, Annals of Pure and Applied Logic, vol. 129 (2004), pp. 1–37.

[13]Jeřábek, E., *The strength of sharply bounded induction*, Mathematical Logic Quarterly, vol. 52 (2006), pp. 613–624.

[14]Jeřábek, E., Approximate counting in bounded arithmetic, this Journal, vol. 72 (2007), pp. 959–993.

[15]Jeřábek, E., *On independence of variants of the weak pigeonhole principle*, Journal of Logic and Computation, vol. 17 (2007), pp. 587–604.

[16]Jeřábek, E., Approximate counting by hashing in bounded arithmetic, this Journal, vol. 74 (2009), pp. 829–860.

[17]Kołodziejczyk, L. A., Nguyen, P., and Thapen, N., *The provably total NP search problems of weak second-order bounded arithmetic*, Annals of Pure and Applied Logic, vol. 162 (2011), pp. 419–446.

[18]Krajíček, J., No counter-example interpretation and interactive computation, In Logic from Computer Science (Moschovakis, Y., editor), vol. 21 (1992), , Springer, Berlin pp. 287–293.

[19]Krajíček, J., Lower bounds to the size of constant-depth propositional proofs, this Journal, vol. 59 (1994), pp. 73–86.

[20]Krajíček, J., Bounded Arithmetic, Propositional Logic and Computational Complexity, Cambridge University Press, 1995.

[21]Krajíček, J., *On the weak pigeonhole principle*, Fundamenta Mathematicae, vol. 170 (2001),pp. 123–140.

[22]Krajíček, J., Pudlák, P., and Takeuti, G., *Bounded arithmetic and the polynomial hierarchy*, Annals of Pure and Applied Logic, vol. 52 (1991), pp. 143–153.

[23]Lauria, M., Short Res*(polylog) refutations if and only if narrow Res refutations, 2011, available at arXiv:1310.5714.

[24]Maciel, A., Pitassi, T., and Woods, A., A new proof of the weak pigeonhole principle, , 2000, pp. 368–377.

[25]Parikh, R., Existence and feasibility in arithmetic, this Journal, vol. 36 (1971), pp. 494–508.

[26]Paris, J., Wilkie, A., and Woods, A., Provability of the pigeonhole principle and the existence of infinitely many primes, this Journal, vol. 53 (1988), pp. 1235–1244.

[27]Pudlák, P., Ramsey’s theorem in bounded arithmetic, In (Börger, E., Büning, H. Kleine, Richter, M., and Schönfeld, W., editors), Springer, Berlin 1991, pp. 308–317.

[28]Pudlák, P., Some relations between subsystems of arithmetic and the complexity of computations, , Springer-Verlag, Berlin 1992, pp. 499–519.

[29]Pudlák, P., *Consistency and games—in search of new combinatorial principles*, In Logic Colloquium ’03 (Stoltenberg-Hansen, V. and Väänänen, J., editors), Lecture Notes in Logic, no. 24, Association of Symbolic Logic, 2006, pp. 244–281.

[30]Pudlák, P. and Thapen, N., *Alternating minima and maxima, Nash equilibria and bounded arithmetic*, Annals of Pure and Applied Logic, vol. 163 (2012), pp. 604–614.

[31]Riis, S., *Making infinite structures finite in models of second order bounded arithmetic*, In Arithmetic, Proof Theory, and Computational Complexity (Clote, P. and Krajíček, J., editors), Oxford University Press, Oxford 1993, pp. 289–319.

[32]Segerlind, N., Buss, S., and Impagliazzo, R., *A switching lemma for small restrictions and lower bounds for k-DNF resolution*, SIAM Journal on Computing, vol. 33 (2004), pp. 1171–1200.

[33]Skelley, A. and Thapen, N., *The provably total search problems of bounded arithmetic*, Proceedings of the London Mathematical Society, vol. 103 (2011), pp. 106–138.

[34]Thapen, N., *A model-theoretic characterization of the weak pigeonhole principle*, Annals of Pure and Applied Logic, vol. 118 (2002), pp. 175–195.

[35]Thapen, N., *Structures interpretable in models of bounded arithmetic*, Annals of Pure and Applied Logic, vol. 136 (2005), pp. 247–266.