Reals and positive partition relations

Abstract

This chapter discusses several remarks and informations about the partition relation. The chapter presents preservation theorem for uncountable cardinals κ. “Standard poset for adding a number of independent reals” means any of the standard posets for adding side-by-side a number of, for example—Cohen, random, Sacks, and Silver reals. The chapter presents a theorem for a certain class of reals, typical members of which are Sacks and Silver reals. The chapter presents the construction of long l-homogeneous sets.