Lexicon of Arguments

Philosophical and Scientific Issues in Dispute
 
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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.

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