Divisibility in beta βN and *N
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RIS BIB ENDNOTEDivisibility in beta βN and *N
Publication date: 08.10.2019
Reports on Mathematical Logic, 2019, Number 54, pp. 65-82
https://doi.org/10.4467/20842589RM.19.003.10651Authors
Divisibility in beta βN and *N
The paper first covers several properties of the extension of the divisibility relation to a set *N of nonstandard integers, including an analogue of the basic theorem of arithmetic. After that, a connection is established with the divisibility in the Stone–Čech compactification βN, proving that the divisibility of ultrafilters introduced by the author is equivalent to divisibility of some elements belonging to their respective monads in an enlargement. Some earlier results on ultrafilters on lower levels on the divisibility hierarchy are illuminated by nonstandard methods. Using limits by ultrafilters we obtain results on ultrafilters above these finite levels, showing that for them a distribution by levels is not possible.
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Information: Reports on Mathematical Logic, 2019, Number 54, pp. 65-82
Article type: Original article
Department of Mathematics and Informatics, Faculty of Sciences University of Novi Sad, 21000 Novi Sad, Serbia
Published at: 08.10.2019
Received at: 16.06.2018
Article status: Open
Licence: CC BY-NC-ND
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English