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How do you call a corollary of a conjecture? Is there a specific name for it? Can it be called simply 'corollary'? Can't it be called 'corollary'?

I mean, does the label 'corollary' imply that the statement it contains is actually true?

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    $\begingroup$ how about consequence ? $\endgroup$ – Tom Collinge Jun 1 '14 at 20:54
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    $\begingroup$ If you follow the Polymath 8/8b project on prime gaps on [Terry Tao's blog][1] you will discover various results described as unconditional, and others as conditional on significant conjectures. There are huge numbers of results conditional on the Riemann Hypothesis (or variants) too. [1]: terrytao.wordpress.com $\endgroup$ – Mark Bennet Jun 1 '14 at 20:59
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    $\begingroup$ Phylosophically speaking, there is no absolute truth, i.e. all propositions have a context to be interpreted in: some kind of axioms in some kind of theory out there are always assumed. In a corollary, the previous theorem/conjecture gives the context. $\endgroup$ – Berci Jun 1 '14 at 21:21
  • $\begingroup$ Thank you for all your comments and suggestions! $\endgroup$ – Vicent Jun 2 '14 at 21:00
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I think it's OK to use "corollary" for a consequence of a conjecture. I would, however, strongly recommend labeling such a statement "Corollary of Conjecture" rather than merely "Corollary". Otherwise, someone who is merely scanning your work and looking for some particular result might see this "corollary" and not realize that it depends on an unproved conjecture. (Worse, that "someone" might be you, 20 years from now.)

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For your second question, according to Online Etymology Dictionary (emphases are mine):

corollary (n.)

late 14c., from Late Latin corollarium "a deduction, consequence," from Latin corollarium, originally "money paid for a garland," hence "gift, gratuity, something extra;" and in logic, "a proposition proved from another that has been proved." From corolla "small garland," diminutive of corona "crown" (see crown (n.)).

While the word typically refers to the consequence of some proven statement, I think it can also mean the consequence of an unproven one too.

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    $\begingroup$ Thanks for the etymology class $\endgroup$ – vonbrand Jun 1 '14 at 23:27
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    $\begingroup$ @vonbrand I was told by Brian Scott that there is such an online etymology dictionary. $\endgroup$ – user1551 Jun 1 '14 at 23:59
  • $\begingroup$ Thank you for all your comments and suggestions! $\endgroup$ – Vicent Jun 2 '14 at 21:01
  • $\begingroup$ How can I say both responses (@Andreas' and @user1551's) answer my question??? $\endgroup$ – Vicent Jun 2 '14 at 21:07
  • $\begingroup$ I think this thread also answers my question, but I am able to mark only one of them as accepted answer. $\endgroup$ – Vicent Jul 8 '14 at 7:59

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