Why Y-c.c

Abstract

We outline a portfolio of novel iterable properties of c.c.c. and proper forcing notions and study its most important instantiations, Y-c.c. and Y-properness. These properties have interesting consequences for partitiontype forcings and anticliques in open graphs. Using Neeman's side condition method it is possible to obtain PFA variations and prove consistency results for them.2000 Mathematics Subject Classification. 03E40.