Three Recursion Theoretic Concepts of Genericity Walter Dean This paper develops and contrasts three recursion-theoretic notions of genericity: one for sets below 0', and two for the recursively enumerable (r.e.) sets. The first is the classical notion of 1-genericity, developed in the context of the finite extension method first developed by Kleene and Post to study degrees below 0'. We review several established facts about 1-generic sets showing that they are bi-immune, generalized low and have Turing incomparable even and odd halves. We then generalize the definition of 1-genericity to obtain a non-effective version of a result of Sacks which states that for any r.e. non-recursive C there is a simple set A such that C <=_T A. We next develop a new notion of genericity based on the Ellentuck-Mathias [EM] topology on 2^\omega. EM-generic sets are shown to be simple and have Turing incomparable even and odd halves. Finally we introduce and generalize a concept of Jockusch known as e-genericity and show how it can be modified so as to obtain the full results of Sacks stated above.