Introduction to Q-Theory

Working in the context of Projective Determinacy (PD), we introduce and study in this paper a countable ∏^1_(2n+1) set of reals Q_(2n+l) and an associated real y^0_(2n+l) for each n ≥ 0 (real means element of ω^ω in this paper). Our theory has analytical (descriptive set theoretic) as well as set theoretic aspects, strongly interrelated with each other.