Book contents
- Frontmatter
- Contents
- Preface
- Continuous Functionals of Dependent and Transfinite Types
- Degree-Theoretic Aspects of Computably Enumerable Reals
- Simplicity and Independence for Pseudo-Algebraically Closed Fields
- Clockwork or Turing U/universe? - Remarks on Causal Determinism and Computability
- A Techniques Oriented Survey of Bounded Queries
- Relative Categoricity in Abelian Groups
- Computability and Complexity Revisited
- Effective Model Theory: The Number of Models and Their Complexity
- A Survey on Canonical Bases in Simple Theories
- True Approximations and Models of Arithmetic
- On the Topological Stability Conjecture
- A Mahlo-Universe of Effective Domains with Totality
- Logic and Decision Making
- The Sheaf of Locally Definable Scalars over a Ring
- Human Styles of Quantificational Reasoning
- Recursion Theoretic Memories 1954–1978
- Fields Definable in Simple Groups
- A Combinatory Algebra for Sequential Functionals of Finite Type
- Model Theory of Analytic and Smooth Functions
Recursion Theoretic Memories 1954–1978
Published online by Cambridge University Press: 17 May 2010
- Frontmatter
- Contents
- Preface
- Continuous Functionals of Dependent and Transfinite Types
- Degree-Theoretic Aspects of Computably Enumerable Reals
- Simplicity and Independence for Pseudo-Algebraically Closed Fields
- Clockwork or Turing U/universe? - Remarks on Causal Determinism and Computability
- A Techniques Oriented Survey of Bounded Queries
- Relative Categoricity in Abelian Groups
- Computability and Complexity Revisited
- Effective Model Theory: The Number of Models and Their Complexity
- A Survey on Canonical Bases in Simple Theories
- True Approximations and Models of Arithmetic
- On the Topological Stability Conjecture
- A Mahlo-Universe of Effective Domains with Totality
- Logic and Decision Making
- The Sheaf of Locally Definable Scalars over a Ring
- Human Styles of Quantificational Reasoning
- Recursion Theoretic Memories 1954–1978
- Fields Definable in Simple Groups
- A Combinatory Algebra for Sequential Functionals of Finite Type
- Model Theory of Analytic and Smooth Functions
Summary
No longer then the storytellers,
We become the story.
-Leo HarringtonNot 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.
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- Chapter
- Information
- Models and Computability , pp. 367 - 376Publisher: Cambridge University PressPrint publication year: 1999