Analytic computable structure theory and \(L^p\)-spaces part 2

  • Tyler Brown
  • Timothy H. McNichollEmail author


Suppose \(p \ge 1\) is a computable real. We extend previous work of Clanin, Stull, and McNicholl by determining the degrees of categoricity of the separable \(L^p\) spaces whose underlying measure spaces are atomic but not purely atomic. In addition, we ascertain the complexity of associated projection maps.


Computable analysis Computable structure theory Functional analysis 

Mathematics Subject Classification

03D45 03D78 46B04 



We thank Diego Rojas for proofreading and several valuable suggestions. We also thank the referee for suggesting many significant improvements.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsIowa State UniversityAmesUSA
  2. 2.Columbia CollegeColumbiaUSA

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