Non-Standard Models for Formal Languages.
The well known Incompleteness Theorem of Godel showed that for any formal axiomatic system S which is adequate for number theory there exists a proposition expressible in S which is undecidable in S. That a proposition expressible in a system is independent of the axioms of the system is not a remar...
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| Language: | en |
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McGill University
1955
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| Online Access: | http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=109996 |
| Summary: | The well known Incompleteness Theorem of Godel showed that for any formal axiomatic system S which is adequate for number theory there exists a proposition expressible in S which is undecidable in S. That a proposition expressible in a system is independent of the axioms of the system is not a remarkable or novel result. Euclid's parallel postulate is independent of the remaining Euclidean axioms of geometry as was shown by the discovery of the non-Euclidean geometries. |
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