Is it possible to have a unique constraint such that one particular column has a value only once?
For instance
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name | pri
You could make a trigger that checks if there allready is a field with the 'TRUE' value, and if so take action.
Note that you cannot easily "reject" the update. (see e.g. : How to abort INSERT operation in MySql trigger? ).
You could for instance just insert it with false, and save your error somehow, by setting a flag.