2023/10/11 by Mazurkiewicz, Łukasz, Żeberski, Szymon
#03E17 (Secondary) #03E75 #28A05 #54H05 (Primary) #FOS: Mathematics #General Topology (math.GN) #Logic (math.LO)
paper · doi:10.48550/arxiv.2310.07693
The aim of this paper is to give natural examples of \mathbfΣ11-complete and \mathbfΠ11-complete sets. In the first part, we consider ideals on ω. In particular, we show that the Hindman ideal H is \mathbfΠ11-complete and consider a number of ideals generated in the similar fashion. Moreover, we show that the ideal D is also \mathbfΠ11-complete. In the second part, we focus on families of trees (on ω and 2) containing a specific tree type. We show the connection between two topics and explore some classical tree types (like Sacks and Miller).