Reflection principles, GCH and the uniformization properties
Jing Zhang
TL;DR
This paper explores the relationship and compatibility between reflection principles and uniformization properties at the second uncountable cardinal, highlighting their contrasting roles in combinatorial set theory.
Contribution
It analyzes the tension and potential compatibility between reflection and uniformization principles at a high cardinal level.
Findings
Reflection principles imply combinatorial guessing properties.
Uniformization properties serve as anti-guessing principles.
The paper discusses conditions for compatibility at the second uncountable cardinal.
Abstract
Reflection principles (or dually speaking, compactness principles) often give rise to combinatorial guessing principles. Uniformization properties, on the other hand, are examples of anti-guessing principles. We discuss the tension and the compatibility between reflection principles and uniformization properties at the level of the second uncountable cardinal.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Homotopy and Cohomology in Algebraic Topology · Computability, Logic, AI Algorithms