Effective Descriptive Set Theory
The area of effective descriptive set theory combines the methods of descriptive set theory with those of generalized recursion theory (especially hyperarithmetical theory). In particular, it focuses on lightface analogues of hierarchies of classical descriptive set theory. Thus the hyperarithmetic hierarchy is studied instead of the Borel hierarchy, and the analytical hierarchy instead of the projective hierarchy. This research is related to weaker version of set theory such as Kripke-Platek set theory and second-order arithmetic.
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Famous quotes containing the words effective, set and/or theory:
“I am sorry to think that you do not get a man’s most effective criticism until you provoke him. Severe truth is expressed with some bitterness.”
—Henry David Thoreau (1817–1862)
“All I’m telling you is that that little creature in there has as much right to live as you do. Don’t forget, you invaded his world. You sank a pipe six miles into the ground and when he climbed up you set dogs on him, shot him.”
—Richard Fielding, and Lee Sholem. Superman (George Reeves)
“If my theory of relativity is proven correct, Germany will claim me as a German and France will declare that I am a citizen of the world. Should my theory prove untrue, France will say that I am a German and Germany will declare that I am a Jew.”
—Albert Einstein (1879–1955)