$ω$-consistency for Different Arrays of Quantifiers
Paulo Guilherme Santos · arXiv (Cornell University) · 2024
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.