Löb's theorem in a set theoretical setting

Studia Logica 75 (3):319 - 326 (2003)
We present a semantic proof of Löb's theorem for theories T containing ZF. Without using the diagonalization lemma, we construct a sentence AUT T, which says intuitively that the predicate autological with respect to T (i.e. applying to itself in every model of T) is itself autological with respect to T. In effect, the sentence AUT T states I follow semantically from T. Then we show that this sentence indeed follows from T and therefore is true.
Keywords Philosophy   Logic   Mathematical Logic and Foundations   Computational Linguistics
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DOI 10.1023/B:STUD.0000009563.84627.cd
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