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Is this sentence correct:

"Politicians often feel obliged to remember or state their achievements because they have various people putting themselves down."

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Christine Christiethey have various people putting themselves them down.

As shown.

The verbs you've used are OK.

Here are more versions of your sentence:

Politicians often feel obliged to state their achievements because so many people want to put them down.
Politicians often feel obliged to remember and state their achievements because others are always trying to put them down.
Politicians often feel obliged to state their achievements frequently because other people are constantly criticizing them.

CJ

Comments  
Christine Christie

Is this sentence correct:

"Politicians often feel obliged to remember or state their achievements because they have various people putting themselves down."

I wonder whether you don't want "Politicians often feel obliged to remind people of their achievements …."