Divisibility in βN and N

• Published in: Reports on mathematical logic Vol. 54; no. 54; pp. 65 - 82
• Main Author: Sobot, Boris
• Format: Journal Article
• Language: English
• Published: Kraków Wydawnictwo Uniwersytetu Jagiellońskiego 2019; Jagiellonian University Press; Jagiellonian University-Jagiellonian University Press
• Subjects: Analytic Philosophy; Enlargement; Logic; Mathematical problems; Methodology and research technology; Theorems; StoneČech compactification; ultrafilter; nonstandard integer; divisibility

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...