Gödel's First Incompleteness Theorem
A consistent effectively axiomatized theory extending Robinson arithmetic cannot decide every sentence. Compare Gödel's omega-consistency argument with Rosser's refinement to separate the hypotheses used in the two proofs.
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first-order sentence · syntactic consistency · Mathematical Induction
Where to read
Start here: Incompleteness and Computability: An Open Introduction to Gödel's Theorems
Richard Zach; based on the Open Logic Text by the Open Logic Project · Open textbook · English · Free full text
§5.3 The First Incompleteness Theorem, Theorem 5.6; §5.4 Rosser's Theorem, Theorem 5.7
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