@article{SAUER1972145,
title = {On the density of families of sets},
journal = {Journal of Combinatorial Theory, Series A},
volume = {13},
number = {1},
pages = {145-147},
year = {1972},
issn = {0097-3165},
doi = {https://doi.org/10.1016/0097-3165(72)90019-2},
url = {https://www.sciencedirect.com/science/article/pii/0097316572900192},
author = {N Sauer},
abstract = {If T is a family of sets and A some set we denote by T ∩ A the following family of subsets of A: T ∩ A = {F ∩ A; F ϵ T}. P. Erdös (oral communication) transmitted to me in Nice the following question: Is it true that if T is a family of subsets of some infinite set S then either there exists to each number n a set A ⊂ S with |A| = n such that |T ∩ A| = 2n or there exists some number N such that |T ∩ A| ⩽ |A|c for each A ⊂ S with |A| ⩾ N and some constant c? In this paper we will answer this question in the affirmative by determining the exact upper bound. (Theorem 2).1}
}

@article{pjm/1102968432,
author = {Saharon Shelah},
title = {{A combinatorial problem; stability and order for models and theories in infinitary languages.}},
volume = {41},
journal = {Pacific Journal of Mathematics},
number = {1},
publisher = {Pacific Journal of Mathematics, A Non-profit Corporation},
pages = {247 -- 261},
year = {1972},
doi = {pjm/1102968432},
URL = {https://doi.org/}
}

@misc{kalai_2008,
title={Extremal Combinatorics III: Some Basic Theorems},
url={https://gilkalai.wordpress.com/2008/09/28/extremal-combinatorics-iii-some-basic-theorems/},
journal={Combinatorics and more},
author={Kalai, Gil},
year={2008},
month={Sep}}

@article {MR0288823,
    AUTHOR = {Vapnik, V. N. and \v{C}ervonenkis, A. Ja.},
     TITLE = {The uniform convergence of frequencies of the appearance of
              events to their probabilities},
   JOURNAL = {Teor. Verojatnost. i Primenen.},
  FJOURNAL = {Akademija Nauk SSSR. Teorija Verojatnoste\u{\i} i ee Primenenija},
    VOLUME = {16},
      YEAR = {1971},
     PAGES = {264--279},
      ISSN = {0040-361x},
   MRCLASS = {60.30},
  MRNUMBER = {0288823},
MRREVIEWER = {R. M. Dudley},
}

