Archive for Mathematical Logic

, Volume 41, Issue 6, pp 507–523 | Cite as

Post's problem for supertasks has both positive and negative solutions

  • Joel David Hamkins
  • Andrew Lewis

Abstract.

 The infinite time Turing machine analogue of Post's problem, the question whether there are semi-decidable supertask degrees between 0 and the supertask jump 0, has in a sense both positive and negative solutions. Namely, in the context of the reals there are no degrees between 0 and 0, but in the context of sets of reals, there are; indeed, there are incomparable semi-decidable supertask degrees. Both arguments employ a kind of transfinite-injury construction which generalizes canonically to oracles.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Joel David Hamkins
    • 1
  • Andrew Lewis
    • 2
  1. 1.Kobe University (Japan); and The College of Staten Island and the CUNY Graduate Center, 365 Fifth Avenue, New York, NY 10016, USA. e-mail: jhamkins@gc.cuny.eduUS
  2. 2.Department of Mathematical Sciences, Virginia Commonwealth University, P.O. Box 842014, Room 2078, Oliver Hall, 1015 West Main Street, Richmond, VA 23284-2014, USA. e-mail: amlewis@saturn.vcu.eduUS

Personalised recommendations