The purpose of this project is to determine whether obstructive sleep apnea (OSA) treatment with positive airway pressure therapy (CPAP) can delay the progression of cognitive impairment in patients with amnestic Mild Cognitive Impairment (MCI) as measured by cognitive testing, and brain magnetic resonance imaging (MRI) scans. Study participants will be assessed at baseline, six-month (cognitive tests only) and one-year follow-up.