Some topics in inner model theory
Lead Research Organisation:
University of Bristol
Department Name: Mathematics
Abstract
The research will focus on ordinal or structural combinatorics in Zermelo-Fraenkel set
theory. This will be concentrating on the interaction of the universe of sets of mathematical
discourse with certain inner models generalising Gödel's universe of constructible sets. We
intend to see how certain large cardinal assumptions about that universe reflect into such
inner models, and alter their properties.
theory. This will be concentrating on the interaction of the universe of sets of mathematical
discourse with certain inner models generalising Gödel's universe of constructible sets. We
intend to see how certain large cardinal assumptions about that universe reflect into such
inner models, and alter their properties.
Organisations
People |
ORCID iD |
| Philip Welch (Primary Supervisor) | |
| Dan Nielsen (Student) |
Studentship Projects
| Project Reference | Relationship | Related To | Start | End | Student Name |
|---|---|---|---|---|---|
| EP/N509619/1 | 01/10/2016 | 30/09/2021 | |||
| 1806686 | Studentship | EP/N509619/1 | 01/10/2016 | 30/06/2020 | Dan Nielsen |
| Description | We have proven that several ostensibly different areas of set theory are in fact highly connected. This concerns the theory of infinite game theory, the study of precipitous ideals, elementary embeddings between set-sized structures and virtual large cardinals. |
| Exploitation Route | This both highlights the natural nature of the virtual large cardinals and smaller large cardinals in general, and provides several new ways of analysing these. |
| Sectors | Other |