Abstract
The sentences that Solovay constructed in his famous theorem on arithmetical completeness of Godel-Lob provability logic are all undecidable. We use Solovay’s method to construct paradoxes, which bear to the Solovay’s sentences much the same relation as the liar paradoxbears to the Godel sentence. The main idea is to use the truth predicate instead of the provability predicate in the formalisation of the Solovay function. A typical example of such paradoxes may be seen as obtained from two ordinary paradoxes by damaging symmetry of the `baptising’ biconditionals. We prove that this paradox is a proper weakening of the latter two in the sense that the former has a strictly lower degree of paradoxicality than the latter two. Solovay’s method provides a new approach to finding various kinds of paradoxes.
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