### An improper arithmetically closed Borel subalgebra of $P(\omega)$ mod FIN

by Enayat and Shelah. [EnSh:936]

Topology and its Applications, 2011

We show the existence of a subalgebra A subset
P (omega) that satisfies the following three
conditions.
A is Borel
(when P (omega) is identified with 2^omega).
A is arithmetically closed (i.e., A is closed under the Turing
jump, and Turing reducibility).
The forcing notion (A, subset) modulo the
ideal FIN of finite sets collapses the continuum to
aleph_0 .

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