Higher indescribability and derived topologies

Abstract: The derived set of a subset of a topological space, also called the Cantor derivative of the set, is the set of limit points of the set. The concept was introduced by Cantor in 1872 and set theory was initially developed in part to study derived sets on the real line. Bagaria (2019) introduced the sequence of derived topologies on an ordinal $\delta$, which are topologies obtained from the interval topology on $\delta$ by declaring certain derived sets to be open. Bagaria used the large cardinal hypothesis of indescribability to show that in some models of set theory the first $\delta$-many derived topologies on $\delta$ can be non-discrete and furthermore the non-isolated points of these spaces can be characterized in terms of reflection properties. We will discuss some natural generalizations of Bagaria’s results. For example, in order to move beyond the first $\delta$-many derived topologies on $\delta$, we introduce diagonal Cantor derivatives and indescribability properties that involve certain kinds of infinitely long sentences.

mathematical physicsanalysis of PDEsclassical analysis and ODEscategory theoryfunctional analysislogicoptimization and controlrepresentation theory

Audience: researchers in the topic

VCU ALPS (Analysis, Logic, and Physics Seminar)

Series comments: Description: Research seminar on topics ranging from analysis and logic to mathematical physics.

Meetings will be conducted over Zoom:

Meeting ID: 951 0562 0974

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