Abstract
In this paper we deal with Fixpoint Arithmetic and Infinite Time Turing Machines. We show that every set of first order assignments definable by a formula of fixpoint arithmetic can be recognized by an Infinite Time Turing Machine, and that the resulting inclusion is proper. Our result, combined with other known results, gives a chain of proper inclusions from Π 1 1 to Fixpoint Arithmetic to Infinite Time Turing Machines to Δ 2 1.
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