2019/10/02 by Šobot, Boris
#03H15 #11U10 #54D35 #54D80 #FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.1910.01094
We continue the research of an extension \widetilde| of the divisibility relation to the Stone-\v Cech compactification βN. First we prove that ultrafilters we call prime actually possess the algebraic property of primality. Several questions concerning the connection between divisibilities in βN and nonstandard extensions of N are answered, providing a few more equivalent conditions for divisibility in βN. Results on uncountable chains in (βN,\widetilde|) are proved and used in a construction of a well-ordered chain of maximal cardinality. Finally, we consider ultrafilters without divisors in N and among them find the maximal class.