Computability Theory and its Applications

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In this project, the P.I. studies problems in both pure andapplied Computability Theory. The problems in pure computabilitytheory are part of the ongoing program to understand the structure ofthe Turing Degrees. As for applied computability theory, the P.I.applies methods from computability theory to study the effectivecontent and proof-theoretical strength of various areas of bothclassical mathematics and foundations of mathematics. He concentratesin problems related to linear orderings, but not exclusively, and alsoworks in effective randomness and computable model theory. Computability Theory is the area of Logic that studies the notionof algorithm. Its applications are based on the idea that problemsthat can be solved using algorithms are simpler than the ones thatcannot. This is used in various ways to measure the complexity ofmathematical objects, theorems, sequences of zeros and ones, etc.. Itis usually the case that this analysis gives a better understanding ofthe subject under study.