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

implications about "size" and countability.

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

implications about "size" and countability.

## Date:

Wed, 19/12/2018 - 14:00 to 15:30

## Location:

Ross 63