Details of Grant 

EPSRC Reference:	GR/A10727/01
Title:	APPROXIMATION FAMILIES AND RELATED CONSTRUCTIONS
Principal Investigator:	Dzamonja, Professor M
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department:	Mathematics
Organisation:	University of East Anglia
Scheme:	Advanced Fellowship (Pre-FEC)
Starts:	01 February 2002	Ends:	31 May 2007	Value (£):	243,675
EPSRC Research Topic Classifications:	Logic & Combinatorics
EPSRC Industrial Sector Classifications:	No relevance to Underpinning Sectors
Related Grants:
Panel History:	Panel Date Panel Name Outcome 16 Nov 2000 Maths Advanced/Senior Fellowship Sifting Panel Deferred
Summary on Grant Application Form
The main area of proposed research is mathematical logic, and the particular subject studied lies within the general area of set theory and its connections with other branches of mathematics. The PI chose several projects to work on during the duration of the proposal: universal models, approximation families and Hrushovski's constructions, SOPS hierarchy, infinitary combinatorial designs, and forcing iterations and cardinal spectra. These projects cover a wide area of subjects, yet they also have a common underlying theme which the PI proposes to explore, that of the construction of infinitary objects using an analogue of Hrushovski's method for uncountable cardinals. Links between the various projects are described in detail in the body of the proposal. The projects build on the areas that the PI has been exploring over the last several years to enter into a broad variety of new subjects.The proposal takes an interdisciplinary approach to problems of interest to several different branches of mathematical logic and mathematics. Many concrete open questions are proposed, and the solutions of these would have an impact on various mathematical communities. The questions proposed here are very challenging and are likely to take years of concentrated effort.
Key Findings
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Potential use in non-academic contexts
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Further Information:
Organisation Website:	http://www.uea.ac.uk