TL;DR
This paper explores the relationships between different orderings of countably complete ultrafilters on ordinals, focusing on how the Ultrapower Axiom influences their linearity and structure.
Contribution
It establishes the equivalence and properties of various ultrafilter orders under the Ultrapower Axiom, advancing understanding of their wellordering and linearity.
Findings
Ultrapower Axiom implies these ultrafilter orders are wellorders.
The orders coincide under the Ultrapower Axiom.
Linearity of ultrafilter orders is characterized by the Ultrapower Axiom.
Abstract
We study various orders on countably complete ultrafilters on ordinals that coincide and are wellorders under a hypothesis called the Ultrapower Axiom. Our main focus is on the relationship between the Ultrapower Axiom and the linearity of these orders.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Computability, Logic, AI Algorithms · Rings, Modules, and Algebras