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Is this sentence correct?

"The analysis of ... has been initiated by ... and settled in full generality by ..."

Or is there a synonym for either "analysis" or "settled in full generality" such that the sentence is correct?

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    It is not clear to me what you are trying to confer. I cannot therefore answer your question. More explanation or an example would greatly help though. – Bookeater Jul 30 '16 at 9:41
  • Well, it is quite hard to provide an example. So the sentence should be part of my introduction in a scientific paper. I want to state that a mathematical problem has been analyzed in full generality (not only for special cases but for any case). – user136457 Jul 30 '16 at 9:59
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    Depends on context. In a mathematical sense "settled in full generality" would mean that the analysis has been conducted in a way that the results are fully applicable to all possible aspects of the issue, vs being limited to some specific subset. – Hot Licks Jul 30 '16 at 12:07
  • There seems to be a problem in the use/s of the word 'analysis' here. Assuming (for example) these definitions from Collins: '4. (Chemistry) chem a. the decomposition of a substance into its elements, radicals, or other constituents in order to determine the kinds of constituents present (qualitative analysis) or the amount of each constituent (quantitative analysis) // b. the result obtained by such a determination >> Your sentence seems to use sense (a) (the investigation ... has been initiated by ...) and then sense (b) (the results of ... – Edwin Ashworth Jul 30 '16 at 23:33
  • the analysis are ...). If this is the case, it's like saying 'Best kicked the ball into, and scored from the resulting, corner.' – Edwin Ashworth Jul 30 '16 at 23:36
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From the English perspective the phrase "settled in full generality" is fairly oxymoronic: -

Generality definition

"...indefinite, unspecific, or undetailed..."

Whereas 'settled in full' implies that the analysis has been thorough, specific, and detailed, to such an extent that no further analysis will yield any fruit.

However the vocabulary here is being used in a specialist technical sense I believe. Generality can also mean (as per 2. in the link above)

An observation or principle having general application; a generalization.

In this case 'full generality' I believe is equivalent to the mathematical expression w.l.o.g (without loss of generality) meaning that the analysis is applicable to a wide variety of cases.

Without loss of generality (often abbreviated to WOLOG, WLOG or w.l.o.g.; less commonly stated as without any loss of generality or with no loss of generality) is a frequently used expression in mathematics... It implies that the proof for that case can be easily applied to all others.

see here

'full generality' would therefore mean the findings of the analysis are applicable universally.

If the phrase is being used in that technical sense, then 'settled' works fine here I would say.

Settled (see definition 10 here)

  1. to conclude or resolve:

Can anlysis be settled? To the extent that is is 'concluded' such that it has provided results applicable to an unrestricted number of fields I would say, yes it can, and this is the context in which the word is being used here I believe.

The setence is asserting that the analysis has been concluded and that the results of the analysis are not restricted to any particular narrow field.

Edit: In relation to comments

"The analysis of ... has been initiated by ... and settled in full generality by ..."

I want to say that the analysis is not restricted to a narrow field but works for all cases,

You could use this phrase for that: -

universally applicable

...but I also want to say that the analysis is thorough. The proofs could be improved (by providing simpler proofs) but the result cannot be improved as it is as general as possible.

In that case I would say the following may well work: -

The analysis of ... has been initiated by ... and satisfactorily resolved (not witholding that a simpler proof may yet be found) to the extent that it has produced findings of universal applicability.

or

The analysis of ... has been initiated by ... and satisfactorily resolved (not witholding that a simpler proof may yet be found) to the extent that it has produced findings that are universally applicable.

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  • Thank you for your long answer. As I am not a native speaker, this is not that easy for me. However, I think that I mean both of the meanings you described above: I want to say that the analysis is not restricted to a narrow field but works for all cases, but I also want to say that the analysis is thorough. The proofs could be improved (by providing simpler proofs) but the result cannot be improved as it is as general as possible. So you would suggest to write "the analysis has been initiated by ... and settled by ..."? – user136457 Jul 30 '16 at 9:56
  • Aha, I see, I have edited to add some additional ideas, in light of your comments. – Gary Jul 30 '16 at 10:05
  • Great! Thank you very much for your help and your suggestions. This is exactly what I was looking for. – user136457 Jul 30 '16 at 10:12
  • Perfect! My pleasure. – Gary Jul 30 '16 at 10:14

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