Talk:Q179692

move "may be identical" claim to another property

@Wikisaurus: You put claims about "may be identical to" other axioms, are you okay that generalization of (P7719) (intended as "implies") is a better property ? author  TomT0m / talk page 17:05, 15 April 2024 (UTC)

Hi! @TomT0m, you are probably right, I did not know about generalization of (P7719) (although I do not understand what claims you talk about). Wikisaurus (talk) 17:15, 15 April 2024 (UTC)

Oh yes, sorry, that was @SMP: I should have pinged, confused the serial edit on the history page. author  TomT0m / talk page 17:18, 15 April 2024 (UTC)

I do not think that it is okay to use generalization of (P7719) because the Axiom of Choice and Zorn's lemma are equivalent while generalization of (P7719) is intended to represent an implication where the first item generalizes the second one. However it is true that the use of said to be the same as (P460) may be unnecessary now that they are implemented as instances of equivalent of the axiom of choice (Q4478785). SMP (talk) 19:46, 15 April 2024 (UTC)

@SMP It's a complicated model and the meaning of equivalent of the axiom of choice (Q4478785) is just provided by linguistic value. But equivalence in logic is just "two way implication" : if A implies (generalizes) B and B implies A then A is equivalent to B. We can retrieve all equivalences by querying, for example by a query along this lines

select ?item ?itemLabel ?equivalent ?equivalentLabel {
  ?item wdt:P7719+ ?equivalent .
  ?equivalent wdt:P7719+ ?item filter (str(?equivalent) < str(?item) ) .
  
  SERVICE wikibase:label { bd:serviceParam wikibase:language "[AUTO_LANGUAGE],en". }
}

Try it!

Except we got an issue with "equivalent of the axiom of choice" because the item is a class of axioms/theorems that appears in the query kind of weirdly and unecessarily, imho. author  TomT0m / talk page 20:23, 15 April 2024 (UTC)