Is There a Nonrecursive Decidable Equational Theory?
 Benjamin Wells
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The ChurchTuring 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 Turingdecidable, 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 Turingdecidable. 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.
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 Title
 Is There a Nonrecursive Decidable Equational Theory?
 Journal

Minds and Machines
Volume 12, Issue 2 , pp 301324
 Cover Date
 20020501
 DOI
 10.1023/A:1015659418145
 Print ISSN
 09246495
 Online ISSN
 15728641
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 ChurchTuring Thesis
 effective procedure
 pseudorecursive theory
 quotidian procedure
 Turing decidability
 Industry Sectors
 Authors

 Benjamin Wells ^{(1)}
 Author Affiliations

 1. Departments of Mathematics and Computer Science, University of San Francisco, San Francisco, CA, USA