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The phrase "a third assumption" is correct and usable in written English.
It can be used when referring to a specific assumption that is the third in a series of assumptions being discussed or analyzed.
Example: "In our analysis, we will consider a third assumption regarding the impact of external factors on the results."
Alternatives: "the third premise" or "a tertiary assumption".
Exact(11)
So I claim I snuck a third assumption.
But I actually made a third assumption, and I made it without telling you.
A third assumption diverges, in general, from the first two by desiring to dispense altogether with the pursuit of defining differences and complementarities between TEK systems and science.
These are the basic, ungrounded entities.[34] Suppose one now adds a third assumption that there is a well-founded ontological dependency structure within the domain of concrete objects.
Finally, and as a third assumption, the bid is placed on the creation and operation of agencies, entities or corporate organizations, and of privatization dynamics, with the aim of achieving new capabilities of management and liability.
A third assumption was that one function of workspace neurons may be to support related processing in more local systems [8] [10].
Similar(48)
A second assumption is potentially even more misleading.
A second assumption is that the financial sector will accept the new arrangements in perpetuity.
The logic of the plan reveals a second assumption that economists make: the more motives the better.
A second assumption was that as the caliphate lost territory in the Middle East, the ISIS brand would gradually lose credibility.
A second assumption is that all effects that match the global signal are of no interest and can be removed.
More suggestions(18)
a third hypothesis
a fifth assumption
a third projection
a third conclusion
a third proviso
a second assumption
a third possibility
a plausible assumption
a third capital
a simplistic assumption
a fatal assumption
a common assumption
a large assumption
a realistic assumption
a third person
a third soldier
a third reason
a fallacious assumption
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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