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@yaarur@mathstodon.xyz

2026-07-01 07:25 UTC

I am very excited to share that I was granted an Academy Research Fellowship by the Research Council of Finland, for my project "Interactions between set theory and non-standard logics"! This is a great honor and great opportunity. The research will be conducted at the University of Helsinki's Department of Mathematics and Statistics, starting September 2026, and will also offer funding for a PhD student (more on this later). Here is the project's public description, feel free to ask questions and read more at the links below. ~~~~ Set theory - the study of collections of objects, which in turn are treated as mathematical objects of their own, can serve as a foundation for all of mathematics. Using the basic axioms governing the behavior of sets, we can prove the existence of practically any known mathematical object. A model of these axioms is a "universe" of sets. However, there is no unique universe of sets - various distinct universes can be constructed. This project examines the ways we can use logic, and in particular "non-standard" logic, to investigate these universes. We focus on two paths, shedding light on the topic from different directions: First, we use modal logic, used to model notions of possibility and necessity, to learn about the interactions between universes which are constructed from one another via the method of "forcing". Second, we use strong logics - extensions of first order logic - to construct smaller universes, and utilize the logic to investigate the results. #math #mathematics #SetTheory #Logic #Academia #grant #RCF #fellowship #UniveristyOfHelsinki

Replies (1)

  • @yaarur@mathstodon.xyz 2026-07-01 07:29

    Links: - RCF Academy Research Fellowships: https://www.aka.fi/en/research-funding/funding-opportunities2/spark-funding/academy-research-fellowship/ - Modal logic of forcing: https://uryaar.com/Digital-garden/Definitions+and+Facts/Modal+Logic+of+Forcing - Inner models from extended logics: https://uryaar.com/Digital-garden/Definitions+and+Facts/Set+theory/Inner+models+from+extended+logics

    Open ##5393425