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The logic of provability. (English) Zbl 0562.03007
This introductory essay gives a survey of the main results of Gödel (1931), Löb (1955), and Sambin (1976) concerning the (un-)provability of certain statements in axiomatic systems (containing enough arithmetics to warrant the procedure of ”Gödel numbering”). The property of provability is then treated as a modal operator, \(\square\), and the resulting theorems of the logic of provability are compared with the standard axioms of \(\square\) interpreted as an alethic modal operator.
Reviewer: W.Lenzen

MSC:
03B25 Decidability of theories and sets of sentences
03B45 Modal logic (including the logic of norms)
03-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mathematical logic and foundations
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