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Is the following sentence acceptable?

The method of invariantly embedding linear orders into ultrapowers is used to find 20 pairwise nonhomeomorphic contonua in BR, under the assumption that the Continuum Hypothesis fails.

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    For the right audience it's probably fine. A little bit long perhaps, but not too long. However as a layman in whatever topic that is, I found it a difficult read anyway. – James Webster Apr 2 '14 at 16:28
  • I'm not sure if it'd still make sense, but I'd consider moving the "under the assumption.." clause to the start. – James Webster Apr 2 '14 at 16:29
  • Does it mean: 'If the Continuum Hypothesis fails, the method of invariantly embedding linear orders into ultrapowers is used to find 20 pairwise nonhomeomorphic continua in BR.' Or 'The method of invariantly embedding linear orders into ultrapowers is used to find 20 pairwise nonhomeomorphic continua in BR. This method depends on the correctness of the assumption that the Continuum Hypothesis is incorrect.'? – Edwin Ashworth Apr 2 '14 at 17:16
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As long as your intended base sentence is "The method is used to find continua," then it is not a run-on. Whether it would benefit from additional clarifying punctuation depends on your intended audience. (And also what most of these words mean.)

  • I wondered if that was the case. Spelling wasn't so much the point of my answer, though. Your independent clause has only one subject ("method"), one verb ("is used to find"), and one object ("continua"), so it is not a run-on. – Wlerin Apr 2 '14 at 16:41

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