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Heterologicality and Incompleteness

✍ Scribed by Cezary Cieśliński

Publisher
John Wiley and Sons
Year
2002
Tongue
English
Weight
128 KB
Volume
48
Category
Article
ISSN
0044-3050

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✦ Synopsis

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 doesn't follow from T and is equivalent (provably in T ) to the consistency of T . Finally we show how to construct a similar incompleteness proof for Peano Arithmetic.

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Incompleteness and Fixed Points
Incompleteness and Fixed Points
✍ Lorenzo Sacchetti 📂 Article 📅 2002 🏛 John Wiley and Sons 🌐 English ⚖ 206 KB

Our purpose is to present some connections between modal incompleteness and modal logics related to the Gödel-Löb logic GL. One of our goals is to prove that for all is incomplete and does not have the fixed point property. As a consequence we shall obtain that the Boolos logic KH does not have the