O'Reilly logo

Effective Mathematics of the Uncountable by Joel David Hamkins, Denis Hirschfeldt, Noam Greenberg

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

INFINITE TIME TURING MACHINES AND AN APPLICATION TO THE HIERARCHY OF EQUIVALENCE RELATIONS ON THE REALS

SAMUEL COSKEY AND JOEL DAVID HAMKINS

Abstract We describe the basic theory of infinite time Turing machines and some recent developments, including the infinite time degree theory, infinite time complexity theory, and infinite time computable model theory. We focus particularly on the application of infinite time Turing machines to the analysis of the hierarchy of equivalence relations on the reals, in analogy with the theory arising from Borel reducibility. We define a notion of infinite time reducibility, which lifts much of the Borel theory into the class in a satisfying way.

Infinite time Turing machines fruitfully extend the operation ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required