Talk:Aczel's anti-foundation axiom

Replace "unique" with "exactly one"

The current formulation "every accessible pointed directed graph corresponds to a unique set" to me seems to be ambiguous, and initially I thought it meant that the "function" from accessible pointed directed graphs to sets is injective. Unless someone objects, (or I forget..) I'll replace it with "every accessible pointed directed graph corresponds to exactly one set". — Preceding unsigned comment added by Susy 11 (talk • contribs) 09:05, 27 January 2022 (UTC)

Replacing "exactly one" with "unique" tripped me up, although that might have been entirely on me. Other sources use "unique" and suddenly seeing "exactly one" made me think this was now saying the mapping was injective (only to realize it wasn't after I already made a quick edit that I now reverted again).

The actual axiom in Peter Aczel (1988) is "Every [directed] graph has a unique decoration." and what the article mentions is just a direct consequence of that. I think the use of "unique" there avoids any ambiguity and would be what I'd prefer to also see here, together with a mention of bisimulation, quotient graphs and some concrete examples so that a reader can get a better idea of what the correspondence between accessible pointed directed graphs and sets looks like. Jannis "jix" Harder (talk) 18:04, 11 December 2024 (UTC)