Finite combinatory processes—formulation

  title={Finite combinatory processes—formulation},
  author={Emil L. Post},
  journal={Journal of Symbolic Logic},
  pages={103 - 105}
  • Emil L. Post
  • Published 1 September 1936
  • Mathematics
  • Journal of Symbolic Logic
The present formulation should prove significant in the development of symbolic logic along the lines of Gödel's theorem on the incompleteness of symbolic logics and Church's results concerning absolutely unsolvable problems. We have in mind a general problem consisting of a class of specific problems. A solution of the general problem will then be one which furnishes an answer to each specific problem. In the following formulation of such a solution two concepts are involved: that of a symbol… 

Recursively enumerable sets of positive integers and their decision problems

Introduction. Recent developments of symbolic logic have considerable importance for mathematics both with respect to its philosophy and practice. That mathematicians generally are oblivious to the

Church-Turing Thesis, in Practice

We aim at providing a philosophical analysis of the notion of “proof by Church’s Thesis”, which is – in a nutshell – the conceptual device that permits to rely on informal methods when working in

Computer Science And Recursion Theory

How recursion theory supplied computer science with specific mathematical definitions and techniques is considered, and how the computer scientist shaped this recursion-theoretic material to his own needs is considered.

The Church-Turing Thesis

The notion of an effective method is an informal one, and attempts to characterise effectiveness, such as the above, lack rigour, for the key requirement that the method demand no insight or

The Invariance Thesis

It is demonstrated that the programs of any classical computation model or programming language that satisfies natural postulates of effectiveness—regardless of the data structures it employs—can be simulated by a random access machine (RAM) with only constant factor overhead.

A Universal Machine without Change of State

The Foundations of Computability Theory

The central notions in this book are those of the algorithm and computation, not a particular algorithm for a particular problem or a particular computation, but the algorithm and computation in

Universality of Wolfram's 2, 3 Turing Machine

The proof I intend to give demonstrates that this Turing machine can emulate any twocolor cyclic tag system for an infinite number of steps and shows that at least one of these initial conditions can be constructed by a process that is clearly not universal itself.

The Developments of the Concept of Machine Computability from 1936 to the 1960s

This chapter tries to show how Turing’s ideas were gradually adopted, developed and modified, and led, toward the end of the century, to profound reflections about the notion of a constructive object and the general notion of an algorithm.


An Unsolvable Problem of Elementary Number Theory

Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use