THE MODEL OF HYPERRATIONAL NUMBERS WITH SELECTIVE ULTRAFILTER

Abstract

In standard construction of hyperrational numbers using ultrapower, we assume that the ultrafilter is selective. This makes it possible to assign the real value to any finite hyperrational number. So, we can consider hyperrational numbers with selective ultrafilter as extension of real numbers field. The existence of strictly monotonic or stationary representing sequence for any hyperrational number is also proved.