Local Compactness for Computable Polish Metric Spaces is \(\varPi ^1_1\)-complete

  • André Nies
  • Slawomir Solecki
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9136)


We show that the property of being locally compact for computable Polish metric spaces is \(\varPi ^1_1\) complete. We verify that local compactness for Polish metric spaces can be expressed by a sentence in \(L_{\omega _1, \omega }\).



This work was carried out at the Hausdorff Institute for Mathematics in October 2013, and at the Research Centre Whiritoa in December 2014.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of AucklandAucklandNew Zealand
  2. 2.Department of MathematicsUniversity of Illinois at Urbana-ChampaignChampaignUSA

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