In keeping with
Does the first part of the following sentence mean " if we follow the theatrical promise of the work we will understand that ..." or "in order to follow the theatrical promise of the work the characters"?

In keeping with the theatrical premise of the work, the characters that represent Salomon’s friends and family were given fictional musical names fitting for an operetta.

Question

In keeping with
Does the first part of the following sentence mean " if we follow the theatrical promise of the work we will understand that ..."  or "in order to follow the theatrical promise of the work the characters"?

In keeping with the theatrical premise of the work, the characters that represent Salomon’s friends and family were given fictional musical names fitting for an operetta.

Answer

It is similar to 'in line with' or 'consistent with'.

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'In keeping' in this sense can mean 'copying', as in you copy what has been done previously like giving family and friends fictional musical names.

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"in keeping with"  identifies a  parameter or boundary for the subject.

It is established that the work  has a "theatrical premise".   The premise defines the boundary of the activity.   The phrase  "in keeping with"   is intended to indicated that the premise is recognizable and that the activity in the theatrical is continued  in the specific context of the parameter established in the premise.