NSF Org:	DMS Division Of Mathematical Sciences
Recipient:	UNIVERSITY OF SOUTH CAROLINA
Initial Amendment Date:	November 1, 1989
Latest Amendment Date:	November 1, 1989
Award Number:	8914426
Award Instrument:	Standard Grant
Program Manager:	Ralph M. Krause DMS  Division Of Mathematical Sciences MPS  Directorate for Mathematical and Physical Sciences
Start Date:	December 1, 1989
End Date:	November 30, 1992 (Estimated)
Total Intended Award Amount:	$40,200.00
Total Awarded Amount to Date:	$40,200.00
Funds Obligated to Date:	FY 1990 = $40,200.00
History of Investigator:	Howard Becker (Principal Investigator) becker@math.sc.edu
Recipient Sponsored Research Office:	University of South Carolina at Columbia 1600 HAMPTON ST COLUMBIA SC  US  29208-3403 (803)777-7093
Sponsor Congressional District:	06
Primary Place of Performance:	DATA NOT AVAILABLE
Primary Place of Performance Congressional District:
Unique Entity Identifier (UEI):	J22LNTMEDP73
Parent UEI:	Q93ZDA59ZAR5
NSF Program(s):	FOUNDATIONS
Primary Program Source:
Program Reference Code(s):
Program Element Code(s):	126800
Award Agency Code:	4900
Fund Agency Code:	4900
Assistance Listing Number(s):	47.049

ABSTRACT

Descriptive set theory is the branch of mathematical logic concerned with definable sets of reals. The research involves several topics in descriptive set theory and in the relationship between descriptive set theory and other parts of mathematics, particularly analysis and topology. Some of these topics will be considered under various types of determinacy assumptions. An outline of the project follows. 1. Classical descriptive set theory and its connections with analysis and topology. 1.1 Classification of pointsets in the projective hierarchy. 1.2 Examples of descriptive set theoretic phenomena occurring in analysis and topology. 1.3 Descriptive set theory and functional analysis: Sequences in Banach spaces. 1.4 Descriptive set theory and topology: Paths, path- connectedness and simple connectedness. 2. Modern descriptive set theory and its connections with other parts of mathematical logic. 2.1 Set theory in the Cabal universe. 2.2 Descriptive set theory in Cabal universe. 2.3 Jump operators and inner model operators.

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