Templates and iterations Luminy 2002 lecture notes (Forcing Method and Large Cardinal Axioms)

This paper is based on part of the lecture notes of a minicourse on iteration techniques presented at the Luminy workshop on set theory in 2002.1The technique of iterations along templates has been developed by Saharon Shelah in 1999 to solve one of the classical problems on cardinal in- variants of the continuum, namely to prove the consistency of D <α [Sh] where D is the dominating number and α is the almost disjointness number.An alternative, axiom atic, treatment of such iterations has been developed by the present author in the survey [Brl] and used in [Br2] to show that a consistently may have countable cofinality.