## Access

You are not currently logged in.

Access JSTOR through your library or other institution:

## If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Journal Article

# Uniform Enumeration Operations

A. H. Lachlan
The Journal of Symbolic Logic
Vol. 40, No. 3 (Sep., 1975), pp. 401-409
DOI: 10.2307/2272164
Stable URL: http://www.jstor.org/stable/2272164
Page Count: 9
Were these topics helpful?

#### Select the topics that are inaccurate.

Cancel
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Preview not available

## 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 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 d. In addition, it is proved that the only other uniform enumeration operations such that d ≤ W (d) for all d are those which equal the identity operation above some fixed degrees.

• 401
• 402
• 403
• 404
• 405
• 406
• 407
• 408
• 409