NSF Org:	DMS Division Of Mathematical Sciences
Recipient:	UNIVERSITY OF NOTRE DAME DU LAC
Initial Amendment Date:	May 27, 1993
Latest Amendment Date:	May 27, 1993
Award Number:	9223767
Award Instrument:	Standard Grant
Program Manager:	Ralph M. Krause DMS  Division Of Mathematical Sciences MPS  Directorate for Mathematical and Physical Sciences
Start Date:	July 1, 1993
End Date:	June 30, 1997 (Estimated)
Total Intended Award Amount:	$91,500.00
Total Awarded Amount to Date:	$91,500.00
Funds Obligated to Date:	FY 1993 = $91,500.00
History of Investigator:	Steven Buechler (Principal Investigator) steven.a.buechler.1@nd.edu
Recipient Sponsored Research Office:	University of Notre Dame 940 GRACE HALL NOTRE DAME IN  US  46556-5708 (574)631-7432
Sponsor Congressional District:	02
Primary Place of Performance:	DATA NOT AVAILABLE
Primary Place of Performance Congressional District:
Unique Entity Identifier (UEI):	FPU6XGFXMBE9
Parent UEI:	FPU6XGFXMBE9
NSF Program(s):	ALGEBRA,NUMBER THEORY,AND COM, FOUNDATIONS
Primary Program Source:	app-0193
Program Reference Code(s):
Program Element Code(s):	126400, 126800
Award Agency Code:	4900
Fund Agency Code:	4900
Assistance Listing Number(s):	47.049

ABSTRACT

Professor Buechler's research is in stability theory, a subfield of model theory. In recent years several general model-theoretic problems have been systematically approached via the stability-theoretic hierarchy. Even though a problem itself may not involve stability-theoretic notions, considering separately the cases: totally transcendental, superstable, etc., brings into play a mass of technical machinery. Such is the case for Vaught's conjecture, which was proved by Shelah for totally transcendental theories and (over the past 5 years) by Buechler for the superstable theories of finite rank. Buechler intends to continue using the methods of geometrical stability theory to gain insight into Vaught's conjecture for all superstable theories. The geometrical methods bring modules into the picture, allowing for the use of representation theory and other algebra to pin down further the models of these theories. This research lies in the general setting of abstract "Classification Theory." In many diverse branches of mathematics researchers attempt to code each element of a class of structures with an element of a "simpler" class of structures. The original class is then more easily analyzed, using the more detailed information that one can obtain for this simpler class. Classification Theory is the abstract study of such codings. Researchers have shown that it is possible to determine when such a simplification exists by using only rather basic information about the original class. Buechler intends to study when an abstract class can be simplified down to a very precise class of objects called "modules," which have been studied in great detail by algebraists.

Please report errors in award information by writing to: awardsearch@nsf.gov.