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I wonder whether there exists a collective term for theorems, lemmas, properties and corollaries?

mdp
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67342343
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    When developing an algorithm I feel the final algorithm is your result and not the properties/lemmas/... that precede it. – 67342343 Jul 18 '13 at 10:59
  • Do you mean proposition rather than property? – Tobias Kildetoft Jul 18 '13 at 11:01
  • When would you use proposition instead of property? – 67342343 Jul 18 '13 at 11:03
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    You would not. But property does not really fit in with the other terms. Proposition does. – Tobias Kildetoft Jul 18 '13 at 11:05
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    This question seems more on topic at english.stackexchange.com, though I suspect it would be a little too vague even there. If anything, I think “theorems” actually does work as a collective term here (excluding properties, as mentioned by others, though). – tomasz Jul 18 '13 at 11:53
  • In mathematical logic, all of these (except properties) are called 'theorems'. More generally, 'sentences'. The difference between a theorem and a sentence is that a theorem is actually true (or provable, depending on the context). A sentence may or may not be true. – goblin GONE Jul 18 '13 at 12:29

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The distinction into axiom, observation, remark, proposition, lemma, corollary, example, theorem, fundamental theorem according to importance of the statement or easiness of proof is rather a matter of taste (except for axioms maybe). Jointly, all these are typically called theorems, that is provable statements (of a particular theory).

Chris Eagle
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Hagen von Eitzen
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  • Clearly, an axiom is deducible, thus a theorem. But in a formal theory, an axiom is distinct from a theorem, in that it is recorded as such. In addition, axiom schemes (and/or proof rules---depending on terminology) have not been mentioned. – 0 _ Dec 20 '17 at 13:36