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I don't think us getting our arses kicked will help.

I don't think our getting our arses kicked will help.

The first is natural to me, a native speaker. But, when considering grammar, which of course can confuse things for me, I realise that the object of the verb think is our/us getting our arses kicked. Therefore, wouldn't it be correct to have the possessive pronoun, not the objective case? Is answer dependent on how formal one wishes to be, or is one correct, while one is not?

Cheers
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The possessive is the strictly grammatically 'correct' one, but as you say, most of us tend to use the object pronoun anyway.
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Thanks.


What about this one then?

The most recent point at which this migration could have taken place is c. 12,000 years ago, with the earliest period remaining a matter of some unresolved contention


OR

with the earliest period's remaining a matter of some unresolved contention