Journal of Symbolic Logic

Uniform Enumeration Operations

A. H. Lachlan

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Abstract

Sacks [2] has asked whether there exists a uniform solution to Post's problem, i.e. an enumeration operation $W$ such that $\mathbf{d} < W(\mathbf{d}) < \mathbf{d}'$ for every degree $\mathbf{d}$. It is shown here that if such an operation $W$ exists it cannot itself in a particular technical sense be uniform. In fact, the jump operation is characterized amongst such uniform enumeration operations by the condition: $\mathbf{d} < W(\mathbf{d})$ for all $\mathbf{d}$. In addition, it is proved that the only other uniform enumeration operations such that $\mathbf{d} \leq W (\mathbf{d})$ for all $\mathbf{d}$ are those which equal the identity operation above some fixed degrees.

Article information

Source
J. Symbolic Logic, Volume 40, Issue 3 (1975), 401-409.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183739472

Mathematical Reviews number (MathSciNet)
MR379156

Zentralblatt MATH identifier
0316.02048

JSTOR
links.jstor.org

Citation

Lachlan, A. H. Uniform Enumeration Operations. J. Symbolic Logic 40 (1975), no. 3, 401--409. https://projecteuclid.org/euclid.jsl/1183739472


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