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A note on incompleteness and heterologicality

✍ Scribed by Peter M. Sullivan


Book ID
110724225
Publisher
Oxford University Press
Year
2003
Tongue
English
Weight
65 KB
Volume
63
Category
Article
ISSN
0003-2638

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πŸ“œ SIMILAR VOLUMES


Heterologicality and Incompleteness
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We present a semantic proof of GΓΆdel's second incompleteness theorem, employing Grelling's antinomy of heterological expressions. For a theory T containing ZF, we define the sentence HETT which says intuitively that the predicate "heterological" is itself heterological. We show that this sentence do

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## Abstract Let __T__ be an extension of Robinson's arithmetic Q. Then __T__ is incomplete even if the set of the GΓΆdel numbers of all axioms of __T__ is βˆ‘~2~.

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## Abstract We give a proof of GΓΆdel's first incompleteness theorem based on Berry's paradox, and from it we also derive the second incompleteness theorem model‐theoretically. Mathematics Subject Classification: 03F30.

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