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The phrase "a second objective" is correct and usable in written English.
You can use it when referring to an additional goal or aim in a discussion or analysis.
Example: "In our project proposal, we outlined a second objective that focuses on improving community engagement."
Alternatives: "an additional goal" or "a secondary aim."
Exact(60)
A second objective is to repeal unimplemented legislation.
A second objective is the direct determination of material data.
A second objective is to learn details regarding several necessary principles required for future CPS.
A second objective was to use PIV to provide experimental data for comparison with mathematical models.
A second objective is to assess the accuracy and practical usage of the reduced global model.
The unemployment threshold, linked to forward guidance, can be seen as a backdoor way of adding a second objective.
Those hawks have long argued that US control of Iraq's oil would help deliver a second objective.
A second objective was to test breed effects on estrus synchronization and superovulation responses.
A second objective was to obtain quantitative data to evaluate the effect of this interaction.
A second objective was to relate these variables to clinical characteristics.
A second objective is to investigate how the inter and intra-tow porosity affect the permeability.
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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