Objective
The project is on the borderline between model theory (mathematical logic) and permutation group theory (algebra), though ideas from other fields such as set theory and combinatorics are involved. The goal is to investigate the following question for a range of first order structures: if one knows the automorphism group Aut(M) of a countable first order structure M, how much is known about M?
The question only makes sense in highly symmetric contexts, such as for omega-categorical structures. Work on reconstruction so far has mainly centred on the small index property, which enables one to recover the topology on Aut(M) from the pure group, and hence to recover M up to bi-interpretability. The proposal is partly to obtain reconstruction results for new classes of structures, by developing new methods for cases where current techniques fail; and partly to prove positive results on a new kind of reconstruction, namely interpretability of a structure in its automorphism group.
The main candidates for investigation are a class of combinatorial constructions due to Hrushovski, which are crucial in model-theoretic simplicity theory, and the class of smoothly approximable structures. The latter have a natural algebraic characterization in terms of covers of classical geometries. The intended methods stem from an approach to reconstruction developed by M. Rubin, which has been neglected in the published literature so far. The proposed approach will involve the notion of generic automorphism, which is highly relevant t o reconstruction and has also independent interest. Applications to reconstruction questions in the non omega-categorical case are envisaged.
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
- natural sciences mathematics pure mathematics discrete mathematics mathematical logic
- natural sciences mathematics pure mathematics topology
- natural sciences mathematics pure mathematics algebra
- natural sciences mathematics pure mathematics geometry
- natural sciences mathematics pure mathematics discrete mathematics combinatorics
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Keywords
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Topic(s)
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Call for proposal
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
FP6-2004-MOBILITY-5
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Funding Scheme
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Coordinator
BARCELONA
Spain
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.