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The phrase "a problem that arises" is correct and usable in written English.
It can be used when discussing issues or challenges that come up in a particular context or situation.
Example: "In any project, a problem that arises can often lead to delays and require immediate attention."
Alternatives: "an issue that emerges" or "a challenge that occurs".
Exact(39)
A problem that arises is that weapons have constituencies.
There's a problem that arises if we have renegotiation.
Entity Resolution (ER) is a problem that arises in many information integration applications.
We consider a problem that arises in the field of frequency domain system identification.
A problem that arises in computer forensics is to determine the type of a file fragment.
A problem that arises is the congestion around gateways, delayed access latency and low throughput.
Similar(21)
All this struck a nerve with me recently, because of a problem that arose with an account I hold with my husband.
The researchers also realized that such natural cleaning might help them cope with a problem that arose once they started transplanting their farmed coral onto the reef.
A problem that arose in this approach was restricted diffusion of oxygen and nutrients leading to cell death in the center of the tissue cubes.
We present a method to solve a verification problem that arises in implementing a commitment strategy for the BDI architecture.
Joyce (2007: 546) uses a causal graph to depict how this may happen in a Newcomb problem that arises in a Prisoner's Dilemma with a psychological twin.
More suggestions(16)
a problem that exists
a problem that pertains
a problem that originates
a problem that concerns
a problem that needs
a problem that increases
a problem that is
a crime that arises
a feature that arises
a problem that has
a confidence that arises
a quality that arises
a problem that goes
a puzzle that arises
a limit that arises
a cancer that arises
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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