Mathematical Sciences: Logical Issues in Constructive       Mathematics, and Metamathematics of Algebra
{'Code': '03040200', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'Ralph M. Krause', 'PO_EMAI': None, 'PO_PHON': None}
Scowcroft's work, in mathematical logic, will center on                    constructive real algebra, the model theory of p-adic fields, and               applications of proof theory to algebra.                                             Having found an effective test for the constructive truth of               propositions, in real algebra, of a bounded logical complexity,                 Scowcroft hopes to isolate a convenient set of axioms for these                 constructively true propositions.  Given such axioms, he would                  like to prove theorems in constructive real algebra by model-                   theoretic means.  Scowcroft also wants to learn whether first-                  order real algebra in Dana Scott's model for intuitionistic                     analysis is recursively undecidable.  Recent work on subanalytic                sets may allow Scowcroft to extend his effective test for                       constructive truth to propositions involving certain                            transcendental functions.                                                            In the model theory of p-adic fields, Scowcroft plans to                   study the properties of definable equivalence relations, the                    differences in expressive power between the first-order languages               commonly used to describe a p-adic field, and possible extensions               of Kochen's theorem on integral-definite rational functions.                         Scowcroft hopes to apply proof-theoretic arguments to obtain               primitive-recursive or elementary bounds for the size of the                    identities given by Kochen's theorem.
{'FirstName': 'Philip', 'LastName': 'Scowcroft', 'PI_MID_INIT': 'H', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Philip H Scowcroft', 'EmailAddress': 'pscowcroft@wesleyan.edu', 'NSF_ID': '000457448', 'StartDate': '07/15/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
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{'Code': '1268', 'Text': 'FOUNDATIONS'}
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