Logic Seminar - Mark Kamsma (UEA)
| Dates: | 16 March 2022 |
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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, Adults, Alumni, Current University students |
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Title: Bilinear spaces over a fixed field are simple unstable
Abstract: We study the model theory of vector spaces with a bilinear form over a fixed field. For finite fields this can be, and has been, done in the classical framework of full first-order logic. For infinite fields we run into issues with compactness and we need a different logical framework. In this talk we will take the approach of positive logic, a framework that is very close to full first-order logic, but where negation is not built in (but can be added as desired). Positive logic allows us to study bilinear spaces over any fixed field. The arising positive theory turns out to be simple unstable. We also fully characterise its existentially closed models. Time permitting, we will also discuss some other interesting facts about this theory, concerning elimination of quantifiers and omega-categoricity.
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Frank Adams 1 (and zoom, link in email)
Alan Turing Building
Manchester
