|Decidability: a question, for example, whether a property applies to an object or not, is decidable if a result can be achieved within a finite time. For this decision process, an algorithm is chosen as a basis. See also halting problem, algorithms, procedures, decision theory._____________Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments. |
|Berka I 331
Undecidability/Predicate calculus 1st level/Gödel: Gödel shows with "Arithmetication" ("Gödelisation") that the predicate calculus of the 1st level is undecidable.
This was a shocking fact for the Hilbert program.
Tarski: (1939) Tarski proved the undecidability of Principia Mathematica and related systems. He showed that it is fundamental, i.e. that it cannot be abolished.
Rosser: Rosser generalized Gödel's proof by replacing the condition of the ω-consistency by that of simple consistency._____________Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution.
K. Berka/L. Kreiser
Logik Texte Berlin 1983