Logic Seminar - Andrew Brooke-Taylor
| Dates: | 11 November 2026 |
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| Times: | 15:00 - 16:00 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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| Who is it for: | University staff, External researchers, Current University students |
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Speaker: Andrew Brooke-Taylor (University of Leeds)
Title: Multiply-generated free shelves of embeddings
Abstract: Large cardinal axioms are axioms that go beyond the usual ZFC axioms for set theory. One of the strongest known ones, referred to as I3, posits the existence of a non-trivial (i.e. not the identity) elementary embedding from an initial segment V_lambda of the universe of sets to itself. There is a way to "apply" such an embedding j to another such embedding k to get another such embedding j*k, and by elementarity, the resulting operation * is self-distributive: j*(k*l)=(j*k)*(j*l). Algebraic structures satisfying this identity are referred to as shelves. Laver showed that the shelf generated by such an embedding with the application operation is in fact the free shelf on 1 generator. After introducing Laver's work, I will talk about recent work with Scott Cramer and Sheila Miller Edwards, showing how one can get a shelf of embeddings that is free on anything up to continuum many generators, from the same assumption I3.
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G.114
Alan Turing Building
Manchester
