Reverse Mathematics and Ramsey's Theorems
Duration: 41 mins 29 secs
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| Description: |
Algebra & Foundations - Recorded 17/04/09 4:00-4:45pm, MR2
Speaker: Julia Erhard |
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| Created: | 2009-07-10 11:30 | ||
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| Collection: | Beyond Part III - Young Researchers in Mathematics 2009 | ||
| Publisher: | University of Cambridge | ||
| Copyright: | A.C. Cullum Hanshaw | ||
| Language: | eng (English) | ||
| Distribution: |
World
(downloadable)
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| Credits: |
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| Explicit content: | No | ||
| Aspect Ratio: | 4:3 | ||
| Screencast: | No | ||
| Bumper: | not set | ||
| Trailer: | not set | ||
| Abstract: | I will give an introduction to the ideas of reverse mathematics and summarise the main results. Reverse mathematics allows us to classify theorems according to their strength. I will place particular emphasis on the classification of Ramsey's Theorem in the context of weak arithmetic. Ramsey's Theorem states that any colouring of the pairs of natural numbers has an infinite monochromatic induced subset. If we colour n-sets (n>2) of natural numbers instead of pairs, the result still holds but is strictly stronger.
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