"As here defined" is an expression used to describe a term or concept that is being specifically explained or interpreted in a particular context. It is often used in academic or technical writing. Some synonyms for this phrase include "as stipulated," "as outlined," "as clarified," "as explained," or "as delineated." Other alternatives might include "as interpreted," "as characterized," "as identified," "as described," or "as specified." Each of these expressions conveys the idea that a particular definition or explanation is being provided in a specific context, and can be used interchangeably with "as here defined" to help facilitate clarity and precision in writing.