  There were two main candidates for new axioms that underwent intensive investigation in the 1970s and 1980s: Axioms of definable determinacy and large cardinal axioms. In this section we will (1) introduce the basic machinery of determinacy and describe the implications of axioms of definable determinacy for classical descriptive set theory and (2) describe the implications of large cardinal axioms for classical descriptive set theory and briefly touch on the connection between the two approaches. 