Mathematical Sciences: Topics in Logic and the Foundations  of Mathematics
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{'SignBlockName': 'Ralph M. Krause', 'PO_EMAI': None, 'PO_PHON': None}
Several research problems and problem areas are under                   investigation, primarily in proof theory, with applications to                  constructive and semi-constructive mathematics and theoretical                  computer science.  In addition a new problem area is proposed,                  relating recursion theory, logic, and algebra.  The topics are as               follows:                                                                        1.  Recursion-theoretic analogues between algebra and logic                     (e.g., Higman's finite embedding theorem and Kleene's finite                    axiomatizability theorem).                                                      2.  Proof-theoretic reduction of subsystems of analysis to weak                 theories.                                                                               (a)  Reduction to PRA and below.                                                (b)  Reduction to PA.                                                   3.  Proof-theory of constructive theories of functions and                      classes.                                                                                (a)  The strength of the general principle of monotone                  inductive definition.                                                                   (b)  The strength of a constructive programming system.                         (c)  Polymorphism.                                                      The interplay between mathematical logic and theoretical computer               science has always been and continues to be very fruitful.
{'FirstName': 'Solomon', 'LastName': 'Feferman', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Solomon Feferman', 'EmailAddress': 'sf@csli.standford.edu', 'NSF_ID': '000462915', 'StartDate': '07/01/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
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{'Code': '1268', 'Text': 'FOUNDATIONS'}
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