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Yes, the schema prefix should not be generated for public Synonyms. I will log a bug on this.
To remove the schema prefix, you can edit the properties for the Synonym and unset the User property.
Alternatively, if you're happy to remove all schema prefixes throughout your DDL file, you could temporarily unset the "Include Schema in DDL" option on the Data Modeler/DDL page of the Preferences.
Note that there is now a forum specifically for Data Modeler issues: SQL Developer Data Modeler
Thank you David. Unsetting the property looks like it will work. Our scripts are designed to run as SYS, so unsetting the "Include Schema in DDL" option will not work for us. I was unaware that there was a special forum for Data Modeler. The "Community" tab on the Data Modeler page brought me here. I've bookmarked it for future use. I appreciate you logging the bug. Thanks again!
This bug has been fixed in Data Modeler version 4.0.2, which can now be downloaded from OTN.