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Can you use the word 'corollary' for an easy consequence of an axiom, or is it a word reserved for consequences of theorems?

Also, if it is not a word for an easy consequence of an axiom, is there a word (or phrase) that would be appropriate in that situation?

IIM
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  • No "standard" terminology; you can see the post: whats-the-difference-between-theorem-lemma-and-corollary. – Mauro ALLEGRANZA Nov 14 '17 at 16:47
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    I looked there, but I wondered if they may only have said 'a corollary is an easy consequence of a theorem' because it did not occur to them that it could also follow from an axiom. – IIM Nov 14 '17 at 16:50
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    According to dictionary, a corollary "is a proposition inferred immediately from a proved proposition with little or no additional proof". Formally an axiom is a theorem (is a theorem with a $1$-line lenght proof). Thus... – Mauro ALLEGRANZA Nov 14 '17 at 16:56
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    Well, in math logic we have axioms, proofs, and theorems; the distinctions between corollary, lemma, proposition, and theorem don't enjoy any formal definitions. It would seem odd to have a corollary to an axiom, just because people don't usually do that, but if you're the independent "go my own way" sort, why not! Otherwise, call it a proposition. – Michael Weiss Nov 14 '17 at 18:03

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