### Saturday, April 9, 2016

#### 9:30 a.m. – 6 p.m. with coffee and lunch breaks

### Virginia Commonwealth University

#### Lectures in Temple 1165

# Itay Neeman : “Forcing with countable conditions”

## Description

The workshop will cover forcing techniques used in the proof that consistently every two ℵ_{2}-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 ℵ_{1}. Baumgartner’s result at ℵ_{1} 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.

Pingback: James Cummings: Proper forcing, side conditions and Baumgartner’s problem | Set Theory Talks