Toward Predicate Approaches to Modality by Johannes Stern

Author:Johannes Stern
Language: eng
Format: epub, pdf
Publisher: Springer International Publishing, Cham

where the function is defined by

and where is either a primitive or a complex one-place predicate of .

If we consider the case where ‘’ is just ‘’ and ‘’ is ‘’, we have the arithmetic interpretation as it is usually presented in stating Solovay’s completeness result.15 Before we give Sololvay’s completeness result, we state that is sound relative to :

Theorem 3.21

For all ,

where of Definition 3.20 is just .

Proof

By induction on the length of a derivation in using Löb’s derivability conditions and Löb’s theorem .

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