# Appalachian Set Theory workshop: Itay Neeman, April 9, 2016

Appalachian set theory

# Itay Neeman : “Forcing with countable conditions”

## Description

The workshop will cover forcing techniques used in the proof that consistently every two ℵ2-dense real order types are isomorphic.

The question is related to the quest for higher analogues for applications of the proper forcing axiom (PFA). It was raised by Baumgartner in the early 1970s, when he proved the analogous result at ℵ1. Baumgartner’s result at ℵ1 is a central consequence of PFA (though it precedes the formulation of PFA by almost a decade) and moreover the methods of his proof have been instrumental for other key applications of PFA.

Projected topics include countable reflection of clubs, sparse sets, and iteration theory for countably closed forcing with side conditions.