How Much Propositional Logic Suffices for Rosser’s Essential Undecidability Theorem?Guillermo Badia (University of Queensland)
Guillerm Badia (UQ) will present "How Much Propositional Logic Suffices for Rosser’s Essential Undecidability Theorem?" at 11 in Old Arts 224 on 13 September.
Abstract: In this talk we explore the following question: how weak can a logic be for Rosser’s essential undecidability to be provable for a weak arithmetic theory? We establish that extending the relevant logic B with weakening (in a language including falsum) is enough. Our work improves on previous results in the literature by Petr Hájek concerning certain fuzzy logics. Hence, Rosser’s argument is seen to go well beyond the scope of the simple Boolean, intuitionistic, or fuzzy case. Our target arithmetical theories are weaker than Robinson’s R and Q but still expressive enough for essential undecidability. (Joint work with Petr Cintula and Andrew Tedder)
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