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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