8 papers
Divisibility classes of ultrafilters and their patterns
Boris Šobot
A divisibility relation on ultrafilters on the set of natural numbers is defined as follows: if and only if…
A survey on divisibility of ultrafilters
Boris Šobot
An extension of the divisibility relation on to the set of ultrafilters on was defined and investigated in several papers during the last te…
-divisibility of ultrafilters II: The big picture
Boris Šobot
A divisibility relation on ultrafilters is defined as follows: if and only if every set in upward closed for div…
More number theory in
Boris Šobot
We continue the research of an extension of the divisibility relation to the Stone-\v Cech compactification . First we prove that ultrafilters we call prime…
Divisibility in *N and
Boris Šobot
The paper first covers several properties of the extension of the divisibility relation to a set of nonstandard integers. After that, a connection is establi…
-divisibility of ultrafilters
Boris Šobot
We further investigate a divisibility relation on the set of ultrafilters on the set of natural numbers. We single out prime ultrafilters (divisible only by 1 and themselves)…
Divisibility orders in
Boris Šobot
We consider five divisibility orders on the Stone-Čech compactification . We find antichains of incompatible elements, and characterize maximal and minimal elements. The main r…
Divisibility in the Stone-Čech compactification
Boris Šobot
After defining continuous extensions of binary relations on the set N of natural numbers to its Stone-Cech compactification βN, we establish some results about one of such extensio…