 Here we imagine that the arrow connectors indicate relative acceptability, thus here, \(j\) (and only \(j)\) is acceptable to \(i\), and \(j\) (and only \(j)\) is acceptable to \(j\). If all worlds that are acceptable to any given world have this property of self-acceptability, then our axiom is valid. For assume that this property holds throughout our models, and for reductio, suppose that for some arbitrary world \(i, \OB (\OB p \rightarrow p)\) is false at \(i\). Then not all \(i\)-acceptable worlds are worlds where \(\OB p \rightarrow p\) is true. So, there must be an \(i\)-acceptable world, say \(j\), where \(\OB p\) is true, but \(p\) is false. Since \(\OB p\) is true at \(j\), then \(p\) must be true at all \(j\)-acceptable worlds. But by stipulation, \(j\) is acceptable to itself, so \(p\) must be true at \(j\), but this contradicts our assumption that \(p\) was false at \(j\). Thus \(\OB (\OB p \rightarrow p)\) must be true at all worlds, after all. Two counter-models showing that \(\OB\)-U is not derivable in SDL, and that SDL \(+ \OB \OB p \rightarrow \OB p\) does not imply \(\OB\)-U can be found in supplement D:  Two Counter-Models Regarding Additions to SDL.