Weak, strong and mixed extensions of relations to spaces of ultrafilters

2025/06/05 by Gasparro, Leonardo Raffaello Maximilian, Baglini, Lorenzo Luperi
#FOS: Mathematics #Logic (math.LO) #Primary: 54D80. Secondary: 03H15

paper · doi:10.48550/arxiv.2506.04692

Abstract

The use of nonstandard methods to characterize properties of weak, strong and mixed extensions of congruences to ultrafilters has been the main topic of several recent papers. We show that similar methods can be used to characterize the extensions of arbitrary realtions and their interplay.

Citations

• Extending orders to types
• A survey on divisibility of ultrafilters
• Self-divisible ultrafilters and congruences in βℤ
• On two types of ultrafilter extensions of binary relations
• On ultrafilter extensions of first-order models and ultrafilter interpretations
• Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory
• Hypernatural Numbers as Ultrafilters

Related

• On two types of ultrafilter extensions of binary relations
• On ultrafilter extensions of first-order models and ultrafilter interpretations
• A Categorical Construction of Ultrafilters
• Notes on ultrafilter extensions of almost bounded structures
• A road to ultrafilter extensions