Work in progress by Michal Walicki
Bergen Logic Seminar: CIRCULARITY AND TRUTH
![Bergen Logic Seminar](https://www.uib.no/sites/w3.uib.no/files/styles/content_main/public/media/bergenlogicseminar.jpg?itok=7PRm-5CV×tamp=1572858065)
Photo:
Colourbox
Main content
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).
15.10.2020