The Y-combinator in Scott''s Lambda-calculus Models

Assume the notation and terminology of Dana Scott's paper "Models for the Lambda-Calculus". In this note I want to exhibit the relationship between the lambda-calculus "paradoxical operator" Y = λx((λy.x(yy))λy.x(yy)) and the minimal fixpoint operator Y* = λx.∞Un=0 xnΩ obtained by regarding the lambda-calculus model as a lattice.