| EPSRC Reference: |
GR/R37388/01 |
| Title: |
Omega-categorical structures and their interpretation in automorphism groups and pseudofinite fields |
| Principal Investigator: |
Macpherson, Professor HD |
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| Department: |
Pure Mathematics |
| Organisation: |
University of Leeds |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
01 November 2001 |
Ends: |
30 April 2004 |
Value (£): |
93,965
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| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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The project consists of pure mathematical research in model theory (a branch of mathematical logic), with connections to set theory, group theory, combinatorics, and number theory. It falls into two parts. Both concern interpreting first order structures which are 'omega-categorical' inside other structures, and the two parts deal with similar examples, but otherwise they have different flavour. In the first, omega-categorical structures will be interpreted inside their automorphism groups, with a view to showing by set-theoretic arguments that the structure is reconstructible from its automorphism group. Related issues on the structure of the automorphism groups will be considered. In the second, omega-categorical structures are interpreted inside 'pseudofinite fields' (infinite models of the theory of finite fields). This should lead to greater understanding of definability in pseudofinite fields. Because of good asymptotic information of definable sets in finite fields, there should be combinatorial applications to classes of finite structures which 'mimic' random structures.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
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| Date Materialised |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.leeds.ac.uk |