Omega-inconsistency without cuts and nonstandard models
AbstractThis 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.
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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: <https://ojs.victoria.ac.nz/ajl/article/view/3900>. Date accessed: 02 july 2020. doi: https://doi.org/10.26686/ajl.v13i5.3900.