2013/05/24 by Adam R. Day, Day, Adam R.
Mathematics · #FOS: Mathematics #Logic (math.LO) #math.LO
paper · pdf · doi:10.48550/arxiv.1305.5858
arxiv created 2013/05/24 · arxiv updated 2013/05/28
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 RCA0). This is the first example of a theorem with this property. It also shows the existence of an almost periodic point is conservative over RCA0 for Pi11 sentences. These results establish the existence of a new upwards-closed subclass of the PA degrees