Notes on the coexistence of limit notions

Abstract

We summarize the current knowledge on the three limit notions: ultrafilter-limits, closed-ultrafilter-limits and FAM-limits. Also, we consider the possibility to perform an iteration which has all the three limits and clarify the problem we face.

arXiv comment19 pages, 2 figures. To appear in RIMS Kôkyûroku, Kyoto University. arXiv admin note: substantial text overlap with arXiv:2401.14600