The Barker Playhouse is a membership theater, where you can’t buy tickets to individual shows unless you know the right person. Anyone can pick up a season-long membership, but the result is an unusually close-knit and very enthusiastic audience. Written by one of the theater’s own members, The Binding Room takes place at a lightly fictionalized version of the Providence Athenaeum. With a set resembling that nearby library’s ground floor, the play deals a nineteenth century Providence library whose trustees decide to auction off rare books in order to finance structural repairs. The Portuguese cleaning woman is played by an actress whose accent reminded me how much I loved Maya Rudolph’s Donatella Versace.