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Bergen Logic Group
Work in progress by Michal Walicki

Bergen Logic Seminar: CIRCULARITY AND TRUTH

Bergen Logic Seminar
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Abstract. We show that extending any FOL language with quantification over all sentences – of the extended language – does not increase expressive power, in particular, does not lead to any paradoxes. Further extension with sentential operators, by a form of definitional extension, does not lead to any pradoxes, either. This allows to extend conservatively every FOL theory with truth operator axiomatized by the single sentence ∀φ(Tφ ↔ φ).