The Logic of Provability and the Incompleteness Theorems
{'Code': '08080301', 'Directorate': {'LongName': 'Direct For Biological Sciences'}, 'Division': {'LongName': 'Div Of Biological Infrastructure'}}
{'SignBlockName': 'Ronald J. Overmann'}
With the work of Hilbert and the publication of the >Principia                  mathematica> by Russell and Whitehead early in this century and                 Godel's work in the 1930's on incompleteness in mathematics, the                issues of provability and incompleteness theorems have been of                  central concern for logicians, mathematicians and philosophers of               mathematics. In 1976, Professor Boolos completed a major study                  which resulted in his book, >The Unprovability of Consistency>.                 Since that time, much has happened in the logic of provability                  which requires a new look at the issues addressed in that                       original study.  Provability logic, a branch of modal logic, is                 the study of those properties of formal consistency and                         provability (as in the work of Hilbert and Godel) that can be                   expressed when a symbol meaning "it is provable that" is added to               the usual languages of logic.  As Godel discovered in his studies               of mathematics, formal provability is a perplexing notion:                      although every interesting formal theory T can prove "2+2=4"                    provable.in.T, no such theory T can prove even "2+2=5"                          >un>provable.in.T.  Provability logic provides a systematic account             of formal provability that makes sense of its strange properties.               The field has grown greatly since 1976.  One striking new feature               of his new study will be the treatment of predicate (i.e.,                      quantified) provability logic, including recent results by                      Artyomov, McGee, Vandanyan and Professor Boolos himself.  This                  and other new topics will greatly enhance our understanding of                  the logic of provability and incompleteness theorems.
{'FirstName': 'George', 'LastName': 'Boolos', 'EmailAddress': '6172534458', 'StartDate': '07/01/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Massachusetts Institute of Technology', 'CityName': 'Cambridge', 'ZipCode': '021394301', 'PhoneNumber': '6172531000', 'StreetAddress': '77 MASSACHUSETTS AVE', 'CountryName': 'United States', 'StateName': 'Massachusetts', 'StateCode': 'MA'}
{'Code': '1353', 'Text': 'Hist & Philosophy of SET'}
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