Mathematical Sciences: Research in Model Theory
{'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}
The principal investigator will continue research in model                 theory that falls under the two general headings of model theory                for ordered structures and monadic second-order logic.                               In research begun several years ago, he studied the notion                 of an o-minimal structure.  This work has unified the model                     theory for several specific classes of linearly ordered                         structures, and has yielded general results known before only in                special cases.  He wishes to consider several questions                         concerning o-minimal structures.  Most importantly, he plans to                 attempt to develop an analogue to stability theory for linearly                 ordered structures, and to investigate the possibilities for a                  general model theory for classes of structures whose natural                    topology is given in a first-order way.                                              The principal investigator also is currently engaged in                    writing a monograph with Y.  Gurevich on monadic second-order                   logic for the "Perspectives in Mathematical Logic" series.  This                book will survey both the rich variety of methods that have been                employed to prove the decidability or undecidability of the                     monadic second-order theory of various structures, and also the                 results that have been obtained using these methods.  The book                  will be written so as to be of interest to both logicians and                   theoretical computer scientists.
{'FirstName': 'Charles', 'LastName': 'Steinhorn', 'PI_MID_INIT': 'I', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Charles I Steinhorn', 'EmailAddress': 'steinhorn@vassar.edu', 'NSF_ID': '000178311', 'StartDate': '07/01/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Vassar College', 'CityName': 'POUGHKEEPSIE', 'ZipCode': '126040001', 'PhoneNumber': '8454377092', 'StreetAddress': '124 RAYMOND AVE', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'New York', 'StateCode': 'NY', 'CONGRESSDISTRICT': '18', 'CONGRESS_DISTRICT_ORG': 'NY18', 'ORG_UEI_NUM': 'J3XVZ8JZRJV8', 'ORG_LGL_BUS_NAME': 'VASSAR COLLEGE', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '1268', 'Text': 'FOUNDATIONS'}
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