On The Strength of Two Recurrence Theorems

This paper uses the framework of reverse mathematics to investigate the strength of two recurrence theorems of topological dynamics. It establishes that one of these theorems, the existence of an almost periodic point, lies strictly between WKL and ACA (working over RCA_0). This is the first example of a theorem with this property. It also shows the existence of an almost periodic point is conservative over RCA_0 for Pi^1_1 sentences. These results establish the existence of a new upwards-closed subclass of the PA degrees