Divisibility in *N and β N
Abstract
The paper first covers several properties of the extension of the divisibility relation to a set *-0.5mmN of nonstandard integers. After that, a connection is established with the divisibility in the Stone-Cech compactification β N, obtaining an equivalent condition for divisibility of ultrafilters introduced by the author. Some earlier results are illuminated by nonstandard methods, and new results on ultrafilters on the higher levels of the divisibility hierarchy are obtained by means of limits.
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