Minds and Machines

, Volume 12, Issue 2, pp 301–324

Is There a Nonrecursive Decidable Equational Theory?

  • Benjamin Wells

DOI: 10.1023/A:1015659418145

Cite this article as:
Wells, B. Minds and Machines (2002) 12: 301. doi:10.1023/A:1015659418145


The Church-Turing Thesis (CTT) is often paraphrased as ``every computable function is computable by means of a Turing machine.'' The author has constructed a family of equational theories that are not Turing-decidable, that is, given one of the theories, no Turing machine can recognize whether an arbitrary equation is in the theory or not. But the theory is called pseudorecursive because it has the additional property that when attention is limited to equations with a bounded number of variables, one obtains, for each number of variables, a fragment of the theory that is indeed Turing-decidable. In a 1982 conversation, Alfred Tarski announced that he believed the theory to be decidable, despite this contradicting CTT. The article gives the background for this proclamation, considers alternate interpretations, and sets the stage for further research.

Church-Turing Thesiseffective procedurepseudorecursive theoryquotidian procedureTuring decidability

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Benjamin Wells
    • 1
  1. 1.Departments of Mathematics and Computer ScienceUniversity of San FranciscoSan FranciscoUSA