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

作者：Enayat Ali^*; Shelah Saharon

来源：Topology and Its Applications, 2011, 158(18): 2495-2502.

DOI：10.1016/j.topol.2011.08.006

• Forcing
• Borel structure
• Tree indiscernible
• Completely separable family

We show the existence of a subalgebra A subset of 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 of) modulo the ideal FIN of finite sets collapses the continuum to (sic)(0).

• 出版日期2011-12-1