Leo Harrington
Encyclopedia
Leo Anthony Harrington is a professor of mathematics at the University of California, Berkeley
who works in
recursion theory
, model theory
, and set theory
.
University of California, Berkeley
The University of California, Berkeley , is a teaching and research university established in 1868 and located in Berkeley, California, USA...
who works in
recursion theory
Recursion theory
Computability theory, also called recursion theory, is a branch of mathematical logic that originated in the 1930s with the study of computable functions and Turing degrees. The field has grown to include the study of generalized computability and definability...
, model theory
Model theory
In mathematics, model theory is the study of mathematical structures using tools from mathematical logic....
, and set theory
Set theory
Set theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics...
.
- Harrington and Jeff ParisJeff ParisJeffrey Bruce Paris is a British mathematician known for his work on mathematical logic, in particular provability in arithmetic, uncertain reasoning and inductive logic with an emphasis on rationality and common sense principles....
proved the Paris–Harrington theoremParis–Harrington theoremIn mathematical logic, the Paris–Harrington theorem states that a certain combinatorial principle in Ramsey theory is true, but not provable in Peano arithmetic...
.
- Harrington showed that if the Axiom of DeterminacyDeterminacyIn set theory, a branch of mathematics, determinacy is the study of under what circumstances one or the other player of a game must have a winning strategy, and the consequences of the existence of such strategies.-Games:...
holds for all analytic setAnalytic setIn descriptive set theory, a subset of a Polish space X is an analytic set if it is a continuous image of a Polish space. These sets were first defined by and his student .- Definition :There are several equivalent definitions of analytic set...
s then x# exists for all reals x.
- Harrington and Saharon ShelahSaharon ShelahSaharon Shelah is an Israeli mathematician. He is a professor of mathematics at the Hebrew University of Jerusalem and Rutgers University in New Jersey.-Biography:...
showed that the first order theory of the partially ordered set of recursively enumerable Turing degrees is undecidable.