Extending the reach of the point-to-set principle

Abstract: The point-to-set principle of J. Lutz and N. Lutz (2018) has recently enabled the theory of computing to be used to answer open questions about fractal geometry in Euclidean spaces R^n. These are classical questions whose statements do not involve computation or related aspects of logic.

I will present the generalization of the point-to-set principle from Euclidean spaces to arbitrary separable metric spaces and to a large class of gauge families.

Then I will demonstrate the power of our extended point-to-set principle by using it to prove new theorems about classical fractal dimensions in hyperspaces.

(The results presented are joint work with Jack Lutz and Neil Lutz).

logic

Audience: researchers in the topic

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Computability theory and applications

Series comments: Description: Computability theory, logic

The goal of this endeavor is to run a seminar on the platform Zoom on a weekly basis, perhaps with alternating time slots each of which covers at least three out of four of Europe, North America, Asia, and New Zealand/Australia. While the meetings are always scheduled for Tuesdays, the timezone varies, so please refer to the calendar on the website for details about individual seminars.

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