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  • Print publication year: 1999
  • Online publication date: May 2010

Recursion Theoretic Memories 1954–1978


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.