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Conservativeness and Incompleteness

✍ Scribed by Shapiro, Stewart

Year
0
Tongue
English
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1 MB
Category
Fiction

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Envelopes, indicators and conservativene
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A well known theorem proved (independently) by J. Paris and H. Friedman states that BΣn+1 (the fragment of Arithmetic given by the collection scheme restricted to Σn+1-formulas) is a Πn+2-conservative extension of IΣn (the fragment given by the induction scheme restricted to Σn-formulas). In this pa

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We present a semantic proof of Gödel'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