There are many results in number theory, where the existence
of some $B \subseteq \mathbb{N}$ with certain properties is proved by
a [probabilistic argument](https://en.wikipedia.org/wiki/Probabilistic_method) employing "random sets". One such example
would be the result of Erdős and Rényi, where they proved the existence
of a "thin" $B\_2[g]$ sequence.


My question is are there certain known properties, so that if $A \subseteq \mathbb{N}$
satisfies them, then $A$ is considered to behave like a random set? or what properties would make $A$ considered to be close to being random? Thank you!



What makes a set random?
One set of answers to these questions is given by the theory of [algorithmic randomness](http://www.scholarpedia.org/article/Algorithmic_randomness).


