arXiv subjects
Publications and source records attributed to Paulo Guilherme Santos.
We study the formalized v statement by allowing the occurrence of different arrays of quantifiers in it. We prove that for some specific arrays of quantifiers we get consistency statements that are S-equivalent to the original $ω$-consistency statement (S denotes the basis theory to develop metamathematics). We end our paper by creating a theory of truth that proves each $ω$-consistency-statement.
In this note we give a simple unifying proof of the undecidability of several diagrammatic properties of term rewriting systems that include: local confluence, strong confluence, diamond property, subcommutative property, and the existence of successor. The idea is to code configurations of Turing Machines into terms, and then define a suitable relation on those terms such that the termination of the Turing Machine becomes equivalent to the satisfiability of the diagrammatic property.