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The phrase "a second problem in" is correct and usable in written English.
It can be used when discussing multiple issues or challenges related to a specific topic or context.
Example: "After addressing the first issue, we encountered a second problem in the implementation phase that needs our attention."
Alternatives: "another issue in" or "a further challenge in".
Exact(11)
There's a second problem in making a movie about any characters active in the distant past.
A second problem in modern physics was the apparent theoretical incompatibility of quantum mechanics with general relativity across very small distances.
A second problem in the ORU-specification is measurement error.
A second problem in transcriptome assembly of ciliates that cannot be grown axenically is that there may be mitochondrial as well as bacterial transcript-related reads mixed in RNA-seq data.
A second problem in SSBV-BLUP is related to the scaling that is done using the SNP frequencies.
As a second problem in describing EMR use, distinguishing EMR from other software or media appeared as a problem in the interviews (theme 4).
Similar(48)
This has given rise to a third problem in addressing climate change, which stems from a combination of the economic implications of the issue and the uncertainty that surrounds it.
A first problem in TTO concerns its feasibility.
A second problem lies in what we conclude from the tests – and what we ignore.
A second problem lies in the sources used -- or not used -- by the authors.
A second problem lies in referring to these thinkers as philosophers.
More suggestions(2)
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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