Mathematical Sciences: Finite Model Theory &amp; Complexity of  Boolean Formulas
{'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}
Woods intends to find theorems giving for any first                        order sentence f the existence of approximations with                           "regular" structure to the set of all models of f with                          universe 1,2,..., n .  (Additional symbols with fixed interpretations           may be allowed to appear in f.)  Woods                                          will obtain these by analyzing the truth tables of Boolean formulas of          restricted logical complexity and possibly by                                   other methods, e.g. p-complete sentences.  He already has                       a result of this nature in the case of purely relational                        sentences and hopes to strengthen it, and to obtain analogous results           for the case where function symbols are also permitted.  His plan is            then to apply these to obtain independence results concerning the               pigeon hole principle in the presence of bounded formula induction,             and to the study of hierarchy problems for spectra or generalized               spectra.
{'FirstName': 'Alan', 'LastName': 'Woods', 'PI_MID_INIT': 'R', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Alan R Woods', 'EmailAddress': None, 'NSF_ID': '000118805', 'StartDate': '02/01/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Yale University', 'CityName': 'NEW HAVEN', 'ZipCode': '065113572', 'PhoneNumber': '2037854689', 'StreetAddress': '150 MUNSON ST', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Connecticut', 'StateCode': 'CT', 'CONGRESSDISTRICT': '03', 'CONGRESS_DISTRICT_ORG': 'CT03', 'ORG_UEI_NUM': 'FL6GV84CKN57', 'ORG_LGL_BUS_NAME': 'YALE UNIV', 'ORG_PRNT_UEI_NUM': 'FL6GV84CKN57'}
{'Name': None, 'CityName': None, 'StateCode': None, 'ZipCode': None, 'StreetAddress': None, 'CountryCode': None, 'CountryName': None, 'StateName': None, 'CountryFlag': None, 'CONGRESSDISTRICT': None, 'CONGRESS_DISTRICT_PERF': '""'}
{'Code': '1268', 'Text': 'FOUNDATIONS'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1987&All=true', 'xml': '8708657.xml'}