Omega-inconsistency without cuts and nonstandard models

  • Andreas Fjellstad University of Aberdeen


This paper concerns the relationship between transitivity of entailment, omega-inconsistency and nonstandard models of arithmetic. First, it provides a cut-free sequent calculus for non-transitive logic of truth STT based on Robinson Arithmetic and shows that this logic is omega-inconsistent. It then identifies the conditions in McGee (1985) for an omega-inconsistent logic as quantified standard deontic logic, presents a cut-free labelled sequent calculus for quantified standard deontic logic based on Robinson Arithmetic where the deontic modality is treated as a predicate, proves omega-inconsistency and shows thus, pace Cobreros et al.(2013), that the result in McGee (1985) does not rely on transitivity. Finally, it also explains why the omega-inconsistent logics of truth in question do not require nonstandard models of arithmetic.


Download data is not yet available.

Author Biography

Andreas Fjellstad, University of Aberdeen
Department of Philosophy
How to Cite
FJELLSTAD, Andreas. Omega-inconsistency without cuts and nonstandard models. The Australasian Journal of Logic, [S.l.], v. 13, n. 5, sep. 2016. ISSN 1448-5052. Available at: <>. Date accessed: 25 jan. 2021. doi: