 Even though the structure of reference involved in Yablo’s paradox does not contain any cycles (each sentence only refers to later sentences in the sequence), it is still being discussed whether the paradox is self-referential or not (Cook, 2014; Halbach and Zhang, 2017). Yablo (1993) himself argues that it is non-self-referential, whereas Priest (1997) argues that it is self-referential. Butler (2017) claims that even if Priest is correct, there will be other Yablo-like paradoxes that are not self-referential in the sense of Priest. In the analysis of Yablo’s paradox, it is essential to note that it involves an infinite sequence of sentences, where each sentence refers to infinitely many other sentences. To formalise it in a setting of propositional logic, it is hence necessary to use infinitary propositional logic. Any finitary variant of Yablo’s sequence—where every sentence only refers to finitely many later sentences in the sequence—must necessarily be consistent (non-paradoxical) due to the compactness theorem in propositional logic (every finite subset of sentences in the sequence induces a well-founded reference relation and the sentences can hence consistently be assigned truth-values bottom-up). In finitary first- and second-order arithmetic, one can instead attempt to formalise Yablo’s paradox by a unary predicate \(S(x)\) where, for every natural numbers \(i\), \(S(\inumeral)\) represents the formalisation of the \(i\)th sentence \(S_i\) of the Yablo sequence (where \(\inumeral\) is the numeral representing \(i)\). How and whether the Yablo paradox can truthfully be represented this way, and how it relates to compactness of the underlying logic, has been investigated by Picollo (2013). 