Lexicon of Arguments

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Berka I 331
Undecidability/Predicate calculus 1st level/Goedel(1931)(1): Goedel shows with the "Arithmetication" ("Goedelisation") that the predicate calculus of the 1st level is undecidable.
>Undecidability, >Gödel numbers.
This was a shocking fact for the Hilbert program.
Tarski (1939)(2): Tarski proved the undecidability of "Principia Mathematica" and related systems. He showed that it is fundamental, i.e. that it cannot be abolished.
Rosser(3): Rosser generalized Goedel's proof by replacing the condition of the ω-consistency by that of simple consistency.
>Consistency.

1. K. Goedel: Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I., Mh. Math. Phys. 38, pp. 175-198.
2. A. Tarski: On undecidable statements in enlarged systems of logic and the concept of truth, JSL 4, pp. 105-112.
3. J. B. Rosser: Extensions of some theorems of Goedel and Church, JSL 1, pp. 87-91.

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