Affiliation:
1. Division of Health, Mathematics, and Sciences, Columbia College, SC, United States of America. tbrown@columbiasc.edu
Abstract
We demonstrate that, within any computable presentation of the Banach space C [ 0 , 1 ], computing 1 is no harder than computing the halting set. Additionally, we prove that the modulus operator | · | is Ø ″ -computable and use this to show that C [ 0 , 1 ] is Δ 3 0 -categorical when we restrict ourselves to the presentations in which at least one homeomorphism of the unit interval onto itself is computable.
Subject
Artificial Intelligence,Computational Theory and Mathematics,Computer Science Applications,Theoretical Computer Science
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