[1]Alon, N., Balogh, J., Morris, R. and Samotij, W. (2014) Counting sum-free sets in Abelian groups. Israel J. Math. 199 309–344.

[2]Bose, R. C. and Chowla, S. (1962/1963) Theorems in the additive theory of numbers. Comment. Math. Helv. 37 141–147.

[3]Cameron, P. J. and Erdős, P. (1990) On the number of sets of integers with various properties. In *Number Theory* (Banff 1988), de Gruyter, pp. 61–79.

[4]Chen, S. (1994) On the size of finite Sidon sequences. Proc. Amer. Math. Soc. 121 353–356.

[5]Chowla, S. (1944) Solution of a problem of Erdős and Turán in additive-number theory. Proc. Nat. Acad. Sci. India. Sect. A 14 1–2.

[6]Cilleruelo, J. (2001) New upper bounds for finite *B*_{h} sequences. Adv. Math. 159 1–17.

[7]Conlon, D. and Gowers, W. T. (2010) Combinatorial theorems in sparse random sets. Submitted.

[8]D'yachkov, A. G. and Rykov, V. V. (1984) *B*_{s}-sequences. Mat. Zametki 36 593–601.

[9]Erdős, P. (1944) On a problem of Sidon in additive number theory and on some related problems: Addendum. J. London Math. Soc. 19 208.

[10]Erdős, P. and Turán, P. (1941) On a problem of Sidon in additive number theory, and on some related problems. J. London Math. Soc. 16 212–215.

[11]Green, B. (2001) The number of squares and *B*_{h}[*g*] sets. Acta Arith. 100 365–390.

[12]Halberstam, H. and Roth, K. F. (1983) Sequences, second edition, Springer.

[13]Hardy, G. H., Littlewood, J. E. and Polya, G. (1934) Inequalities, Cambridge University Press.

[14]Janson, S., Łuczak, T. and Ruciński, A. (2000) Random Graphs, Wiley-Interscience.

[15]Jia, X. D. (1993) On finite Sidon sequences. J. Number Theory 44 84–92.

[16]Kleitman, D. J. and Wilson, D. B. (1996) On the number of graphs which lack small cycles. Unpublished Manuscript.

[17]Kleitman, D. J. and Winston, K. J. (1982) On the number of graphs without 4-cycles. Discrete Math. 41 167–172.

[18]Kohayakawa, Y., Lee, S. J., Rödl, V. and Samotij, W. (2015) The number of Sidon sets and the maximum size of Sidon sets contained in a sparse random set of integers. Random Struct. Alg. 46 1–25.

[19]Kohayakawa, Y., Lee, S. and Rödl, V. (2011) The maximum size of a Sidon set contained in a sparse random set of integers. In *Proc. Twenty-Second Annual ACM–SIAM Symposium on Discrete Algorithms* (Philadelphia, PA), SIAM, pp. 159–171.

[20]Kohayakawa, Y., Łuczak, T. and Rödl, V. (1996) Arithmetic progressions of length three in subsets of a random set. Acta Arith. 75 133–163.

[21]Kolountzakis, M. N. (1996) The density of *B*_{h}[*g*] sequences and the minimum of dense cosine sums. J. Number Theory 56 4–11.

[22]Krückeberg, F. (1961) *B* _{2}-Folgen und verwandte Zahlenfolgen. J. Reine Angew. Math. 206 53–60.

[23]Lee, S. J. On Sidon sets in a random set of vectors. *J. Korean Math. Soc.*, to appear.

[24]Lindström, B. (1969) A remark on *B* _{4}-sequences. J. Combin. Theory 7 276–277.

[25]O'Bryant, K. (2004) A complete annotated bibliography of work related to Sidon sequences. *Electron. J. Combin.* Dynamic Surveys **11** (electronic).

[26]Roth, K. F. (1953) On certain sets of integers. J. London Math. Soc. 28 104–109.

[27]Saxton, D. and Thomason, A. (2015) Hypergraph containers, Invent. Math., 201 925–992

[28]Schacht, M. Extremal results for random discrete structures. Submitted.

[29]Shparlinskii, I. E. (1986) On *B*_{s}-sequences. In Combinatorial Analysis, no. 7 (Russian), Moscow State University, pp. 42–45.

[30]Singer, J. (1938) A theorem in finite projective geometry and some applications to number theory. Trans. Amer. Math. Soc. 43 377–385.

[31]Szemerédi, E. (1975) On sets of integers containing no *k* elements in arithmetic progression. Acta Arith. 27 199–245.