Correction to A note on the Entscheidungsproblem

  title={Correction to A note on the Entscheidungsproblem},
  author={Alonzo Church},
  journal={Journal of Symbolic Logic},
  pages={101 - 102}
  • A. Church
  • Published 1 September 1936
  • Mathematics
  • Journal of Symbolic Logic
In A note on the Entscheidungsproblem the author gave a proof of the unsolvability of the general case of the Entscheidungsproblem of the engere Funktionenkalkül. This proof, however, contains an error, in order to correct which it is necessary to modify the “additional axioms” of the system L so that they contain no free variables (either free individual variables or free propositional function variables). The additional axioms of L other than x=y→[F(x)→F(y)] contain no free propositional… 

On the Remarkable Features of Binding Forms

A new kind of classification based on the binding forms that are admitted in a sentence, i.e., on the way the arguments of a relation can be bound to a variable is introduced, showing that the less expressive one is already incomparable with the guarded logic and related extensions.

Maximal Models and Refutation Completeness: Semidecision Procedures in Automatic Theorem Proving*

In recent years the idea of using electronic computers to search for proofs of theorems of quantification theory has drawn considerable attention. One of the more successful methods of attack on the

From Solvability to Formal Decidability: Revisiting Hilbert’s “Non-Ignorabimus”

The topic of this article is Hilbert’s axiom of solvability, that is, his conviction of the solvability of every mathematical problem by means of a finite number of operations. The question of

Lambda calculus and Functional Programming

1.1 (HW) a) Write explicitely as lambda-abstractions (including parentheses, dots, etc.), with all parentheses, with only necessary parentheses, and reduce: a.1) KII ; a.2) K(IK∗)I b) Explain: KA 6=

Related Citations

  • Philosophy
    Journal of Symbolic Logic
  • 1937
chief objection to interpreting general propositions, even ideally, as conjunctions and disjunctions. Suppose that we could write down an infinite conjunction or disjunction. That would be of no use,

A Natural Axiomatization of Church's Thesis

The Abstract State Machine Thesis asserts that every classical algorithm is behaviorally equivalent to an abstract state machine. This thesis has been shown to follow from three natural postulates

On the Decision Problem for Two-Variable First-Order Logic

Improve Mortimer's bound by one exponential and show that every satisfiable FO2-sentence has a model whose size is at most exponential in the size of the sentence, establishing that the satisfiability problem for FO2 is NEXPTIME-complete.

Turing-machines and the Entscheidungsproblem

Let Q be the set of all sentences of elementary quantification theory (without equality). In its semantic version Hilbert’s Entscheidungsproblem for a class X ⊇ Q of sentences is, [X]: To find a

Meaning, Reality and Algorithms: Implications of the Turing Theorem

The theorems of Kurt Godel and Alan Turing are likely to be remembered as the two most important achievements in mathematics of the twentieth century. Their far-reaching consequences are valid for

Conceptual Confluence in 1936: Post and Turing

It is argued that the unity of their approach is of deep significance for the theory of computability and not to be viewed as a surprising coincidence, but rather as a natural consequence of the way in which Post and Turing conceived of the steps in mechanical procedures on finite strings.



A note on the Entscheidungsproblem

  • A. Church
  • Mathematics
    Journal of Symbolic Logic
  • 1936
It is shown that the general case of the Entscheidungsproblem is unsolvable in any system of symbolic logic which is adequate to a certain portion of arithmetic and is ω-consistent.

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