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The phrase "acknowledge that the first" is correct and usable in written English.
It can be used when you want to recognize or admit something that is the first in a series or category.
Example: "In our discussion, we must acknowledge that the first step towards improvement is recognizing our weaknesses."
Alternatives: "recognize that the first" or "admit that the first".
Exact(9)
"We had to tip our hand and acknowledge that the first movie was out there.
Navy officials acknowledge that the first prototype weapon to be deployed is not powerful enough to take on jet fighters or missiles on their approach.
At a lunch with reporters upstate last week, Mr. Lazio seemed to acknowledge that the first debate had not gone as well as his advisers had originally claimed.
1 Guantánamo Trial Challenges Officials acknowledge that the first full war crimes trial before a military tribunal at Guantánamo is in turmoil and say there will be substantial changes made in coming weeks.
His aides acknowledge that the first task is to answer those senators, former generals and an older generation of national security experts who ask why there is such urgency to confront Iraq now.
But I have to acknowledge that the first chapter of The Daughters of Mars is titled "Murdering Mrs. Durance".
Similar(48)
Still, some security officials acknowledge that the second pass is not always checked.
(Though functionalists of course acknowledge that the first-order states that satisfy the functional definitions may vary from species to species — or even from individual to individual — they specify that, for each individual, the functional definitions be uniquely satisfied).
We acknowledge that the second model is to be preferred over the first model that ignores origin.
Manning threw interceptions on the first two possessions against Chicago and acknowledged that the first came on a poor read.
His method acknowledges that the first duty of television is to prevent the ruthless viewer switching off.
More suggestions(19)
agree that the first
recognize that the first
confirm that the first
acknowledge that the worst
acknowledge that the largest
appreciate that the first
acknowledges that the first
recognise that the first
recognition that the first
confirmed that the first
emphasize that the first
recognizing that the first
acknowledge that the biggest
identify that the first
acknowledge that the strongest
acknowledging that the first
recognized that the first
acknowledge that the current
acknowledge that the very
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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