  The independence results of Gödel and Cohen thus showed that if one wished to develop descriptive set theory further then one must invoke additional axioms. There were two main approaches, each of which led to a rebirth of descriptive set theory. The first approach was to invoke axioms of definable determinacy. The axiom of determinacy (AD) was introduced by Mycielski and Steinhaus in 1962 and it was quickly seen to yield generalizations of the results of classical descriptive theory. Unfortunately, AD contradicts AC and for this reason it was never really proposed as a new axiom. However, Solovay and Takeuti pointed out that there is a natural such subuniverse, namely, L(ℝ), in which AD could hold, consistently with assuming AC in the full universe. This led to a hierarchy of axioms of definable determinacy that underwent intensive investigation in the 1970s and 1980s. The main sources for this period are Moschovakis (1980) and the volumes of the Cabal seminar during 1977–1985. The second approach was to invoke large cardinal axioms. This approach was initiated by Solovay in 1965. Finally, in the late 1960s Solovay conjectured that large cardinal axioms actually imply axioms of definable determinacy. If true, this would open the way for a unification of the two approaches. This hope was realized in the work of Martin, Steel, and Woodin from 1984 onward. 