MINCONDINMT · Minimality conditions in model theory
FP6 — Marie Curie Actions (Human Resources and Mobility)
- Duration
- 2004-04-01 → 2006-03-31
- EU contribution
- €152,809
- Participants
- 1
- Scheme
- EIF
Lines connect the coordinator with its partners.
Results in brief
Final Activity Report Summary - MINCONDINMT (Minimality conditions in model theory)
Wencel developed the model theory of Boolean algebras and their expansions, under a restriction on definable sets, and investigated elimination of imaginaries in Boolean algebras. He also greatly extended the current theory of weakly o-minimal totally ordered first order structures. Key results concern the good behaviour of topological dimension, and understanding of certain well-behaved weakly o-minimal structures (those with the 'strong cell decomposition property'). He proved that algebraic objects living definably in weakly o-minimal structures carry definably a topology related to their algebraic structure. These results form a significant contribution to model theory, a branch of mathematical logic, and its connections to topology. Their context is a programme to understand topological first order structures in which definable sets (solution sets of first order formulas) have a natural form, at least in one variable. A striking and unexpected development was a connection to number theory, for example to the Gelfond-Schneider Theorem that if a,b are algebraic numbers with a not equal to 0 or 1 and b not a rational, then a^b, the bth power of a, is trancendental.
Data: CORDIS, © European Union
Project objective
The main objective of this proposal is to continue tee study general model theoretic properties and examples of important classes of structures which are minimal with respect to a certain language, namely weakly o-minimal, C-minimal and P-minimal structures and o-minimal expansions of Boolean algebras. Each of these classes is constrained by certain tight conditions on definable sets in one variable. In the case of weak o-minimalist, especially for weakly o-minimal expansions of real closed fields without definable valuations and expansions of o-minimal structures by convex predicates, I plan to investigate various geometric and topological concepts (like Eller characteristics, smoothness and fineries properties) for definable sets. I will also study definable groups, the theory of weakly o-minimal ordered fields, elimination of imaginaries and expansions of weakly o-minimal structures by convex predicates. I am going to apply techniques developed for weakly o-minimal structures to approach relevant questions concerning C- and P-minimal structures. I am also planning to generalize results (concerning o-minimal expansions of Boolean algebras) from my PhD thesis. I will be mainly working with Prof. McPherson and Prof. Truss, leading specialists in the area of variants of o-minimalist. A part of my PhD thesis is closely related to the research of Prof. Truss (concerning the small index property). Therefore I believe that the results from my PhD thesis and their planned extension will be of great interest to the Leeds model theory group. Through undertaking this project my research will develop smoothly from the area of my PhD to topics (o-minimalist and variants of this notions) intensively studied by many European model theorists. The training through research and through interactions in Leeds will leave me excellently placed for a permanent academic position and will develop a solid base for further cooperation in research.
Original text from CORDIS.
Participants
- UNIVERSITY OF LEEDS · LEEDSCoordinatorUnited Kingdom
Links
Data: CORDIS, © European Union