Affiliation:
1. School of Philosophy, Wuhan University , Wuhan, China
Abstract
Abstract
In this work, we aim at understanding incompleteness in an abstract way via metamathematical properties of formal theories. We systematically examine the relationships between the following twelve important metamathematical properties of arithmetical theories: Rosser, EI (effectively inseparable), RI (recursively inseparable), TP (Turing persistent), EHU (essentially hereditarily undecidable), EU (essentially undecidable), Creative, $\textbf{0}^{\prime }$ (theories with Turing degree $\textbf{0}^{\prime }$), REW (all RE sets are weakly representable), RFD (all recursive functions are definable), RSS (all recursive sets are strongly representable), RSW (all recursive sets are weakly representable). Given any two properties $P$ and $Q$ in the above list, we examine whether $P$ implies $Q$.
Publisher
Oxford University Press (OUP)
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