 The set-theoretic formulation of well-foundedness is the sense in which, e.g., Fine (2010: 100) appears to use the notion. Applied to chains of grounding, the proposal is that well-foundedness would rule out infinite, non-terminating grounding chains and entail that “the grounds of any truth that is grounded will “bottom out” in truths that are ungrounded”. We can see slightly different but equivalent formulations in Schaffer (2010a, 37), Bennett (2011a, 30), Trogdon (2013: 108), Tahko (2014: 260), Dixon (2016: 452), and Jago  (2018).[20]  As Dixon (ibid.) puts it, the attraction of using the set-theoretic notion of well-foundedness is that it is a straightforward application of the standard mathematical definition of a well-founded relation (this is also recognized by Morganti 2015: 556fn2). The only problem is that the standard understanding of well-foundedness may be too strict for the task at hand. Many authors have considered weakened versions of the well-foundedness requirement, which may be more suitable for expressing the desired limits on infinite grounding chains (R. Cameron 2008: 4; Trogdon 2013: 108; Leuenberger 2014: 170–171). So, to summarize, it might at first seem intuitive to interpret well-foundedness simply as a ban on infinite chains and cycles of grounding, in accordance with set-theoretic well-foundedness. But this would seem to go against the intuition that there are cases of infinite chaining which are acceptable for the foundationalist metaphysician (R. Cameron 2008; Bliss 2013). This has recently been made explicit by Dixon (2016) and Rabin &amp; Rabern  (2016).[21]