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The phrase "extension to the" is grammatically correct and can be used in written English.
It is commonly used when talking about expanding or adding on to something. Example: The company announced an extension to the existing office building, with plans to add a new wing for additional workspaces.
Exact(60)
An extension to the algorithm incorporates spilling.
Republicans may demand an extension to the Bush tax cuts.
Also included is an extension to the stochastic case.
The segmentation network is an extension to the classification net.
This is an extension to the standard mixture design problem.
Can I get an extension to the well plugging requirement?
One popular extension to the standard model is supersymmetry.
Last year Westminster council authorised a large extension to the house.
The No. 7 subway extension to the far West Side of Manhattan is under construction.
Greek politicians have been pressing for an extension to the deadline for meeting its targets.
A new airport is opening soon, as is an extension to the city's metro train system.
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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