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"the second assumption" is a correct and usable phrase in written English.
It can be used when referring to any kind of assumption that comes after the first one. For example, "The first assumption was that the party would be a success, but the second assumption proved to be incorrect when only a handful of people showed up."
Exact(59)
The second assumption is what troubles Messrs Krusell and Smith.
The second assumption should be if they want to stay, they should reach out.
What about the second assumption — that Google's free online software can do everything you'd ever want?
The second assumption was to suppose that this homogeneous and isotropic universe had a closed spatial geometry.
The second assumption is also unlikely.
The second assumption is that of locality.
No speculation is needed on the second assumption.
The second assumption ensures the identifiability of harmonic phases.
Table 4 shows the accuracy of the second assumption.
By the second assumption, we have (theta >0).
The second assumption concerns the identification of the shock.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com