Skip to main content Accessibility help
×
Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-05T05:28:23.111Z Has data issue: false hasContentIssue false

Recursion Theoretic Memories 1954–1978

Published online by Cambridge University Press:  17 May 2010

S. Barry Cooper
Affiliation:
University of Leeds
John K. Truss
Affiliation:
University of Leeds
Get access

Summary

No longer then the storytellers,

We become the story.

-Leo Harrington

Not a history lesson. Am not a historian nor was meant to be. A personal memoir, an attempt to recall faint impressions of recursion theoretic events. Recursion theory is a house with many rooms. Today I open the door on classical recursion theory, the science of recursively enumerable sets and degrees, far less so on higher recursion theory, and only from 1954 to 1978. I also turn the light on some personal recursion theoretic struggles during those distant days. Not a survey paper, but a partial reconstruction of what caught my recursion theoretic eye back then. Nature being what it is, I have overlooked a great deal. Here is my list.

Incomparable Degrees. There exist incomparable Turing degrees below 0′ (Kleene and Post 1954). My first year of graduate study was 1958-59. My thesis advisor, J. B. Rosser, conducted a two-hour logic seminar once a week. I was the only student, although one or two Cornell faculty members occasionally attended. Rosser was the principal speaker in the fall. He talked about many-valued logic, set theory, lambda calculus and combinatory logic. At first I thought he preferred formal syntactical arguments, but then he surprised me with slick algebraic proofs of completeness for many-valued systems. Without saying so explicitly, he taught me that logic was just another branch of mathematics to which ideas from other branches could be applied.

Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 1999

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×