The theory PA(aa), which is Peano Arithmetic in the context of stationary logic, is shown to be consistent. Moreover, the first-order theory of the class of finitely determinate models of PA(aa) is characterized.
"PA(aa)." Notre Dame J. Formal Logic 36 (4) 560 - 569, Fall 1995. https://doi.org/10.1305/ndjfl/1040136916