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Volume 24 - Issue 2 - June 2018

Bulletin of Symbolic Logic Volume 24 - Issue 2 -
Contents

Page 1 of 2

Articles

  • STRONG JUMP-TRACEABILITY

  • NOAM GREENBERG, DAN TURETSKY
  • Published online by Cambridge University Press:
    07 August 2018, pp. 147-164

  • We review the current knowledge concerning strong jump-traceability. We cover the known results relating strong jump-traceability to randomness, and those relating it to degree theory. We also discuss the techniques used in working with strongly jump-traceable sets. We end with a section of open questions.

  • PERMUTATIONS OF THE INTEGERS INDUCE ONLY THE TRIVIAL AUTOMORPHISM OF THE TURING DEGREES

  • BJØRN KJOS-HANSSEN
  • Published online by Cambridge University Press:
    07 August 2018, pp. 165-174

  • Is there a nontrivial automorphism of the Turing degrees? It is a major open problem of computability theory. Past results have limited how nontrivial automorphisms could possibly be. Here we consider instead how an automorphism might be induced by a function on reals, or even by a function on integers. We show that a permutation of ω cannot induce any nontrivial automorphism of the Turing degrees of members of 2ω, and in fact any permutation that induces the trivial automorphism must be computable.

    A main idea of the proof is to consider the members of 2ω to be probabilities, and use statistics: from random outcomes from a distribution we can compute that distribution, but not much more.

Reviews

In Memoriam

  • IN MEMORIAM: MATI RUBIN 1946–2017

  • Assaf Hasson, Robert Bonnet
  • Published online by Cambridge University Press:
    07 August 2018, pp. 181-185
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  • IN MEMORIAM: VLADIMIR VOEVODSKY 1966–2017

  • Daniel R. Grayson
  • Published online by Cambridge University Press:
    07 August 2018, pp. 186-191
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Thesis Abstracts

  • Reverse Mathematics and Partial Orders, University of Udine, Italy, 2014. Supervised by Alberto Marcone

  • Emanuele Frittaion
  • Published online by Cambridge University Press:
    07 August 2018, p. 196
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  • Some Results on Tight Stationarity, University of California, Los Angeles, USA, 2016. Supervised by Itay Neeman

  • William Chen
  • Published online by Cambridge University Press:
    07 August 2018, pp. 198-199
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  • Believing in Logic and Philosophy, KU Leuven, Belgium, 2014. Supervised by Stefaan Cuypers

  • Lorenz Demey
  • Published online by Cambridge University Press:
    07 August 2018, pp. 201-202
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