2018
Dec
19

# Set Theory Seminar - Asaf Karagila (The Morris model)

2:00pm to 3:30pm

## Location:

Ross 63

Title: The Morris model

Abstract: Douglass Morris was a student of Keisler, and in 1970 he announced the

following result: It is consistent with ZF that for every \alpha, there is a set

A_\alpha which is the countable union of countable sets, and the power set of

A_\alpha can be partitioned into \aleph_\alpha non-empty sets.

The result was never published, and survived only in the form of a short

announcement and an exercise in Jech's "The Axiom of Choice". We go over the

proof of this theorem using modern tools, as well as some of its odd

Abstract: Douglass Morris was a student of Keisler, and in 1970 he announced the

following result: It is consistent with ZF that for every \alpha, there is a set

A_\alpha which is the countable union of countable sets, and the power set of

A_\alpha can be partitioned into \aleph_\alpha non-empty sets.

The result was never published, and survived only in the form of a short

announcement and an exercise in Jech's "The Axiom of Choice". We go over the

proof of this theorem using modern tools, as well as some of its odd