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Changing Images in Mathematics by Amy Dahan Dalmedico, Umberto Bottazini

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Chapter 10 DEFINABILITY AS A MATHEMATICAL CONCEPT BEFORE AND AFTER GÖDEL

Gabriele Lolli

 

 

In the opinion of most commentators, either logicians or mathematicians, the importance and influence of Gödel's incompleteness results were nil. According to Kreisel [1988], Gödel's theorems have had absolutely no use, and properly so, since they were tailored to refute— or confirm, it does not matter—a specific thesis about the completeness of mathematical systems. Bourbaki [1960] dutifully recalled Gödel's two incompleteness theorems, but only in the historical notes of the section ‘Metamathematics’ and nowhere else in the treatise. The theorems were likewise seen as a negative answer to Hilbert's program. Bourbaki hinted at their proofs and the ...

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