Database is the essence of Notion. Oopy determine the permission of a database with 3 simple rules.
3 rules
1.
Permission of a database inherits from the belonging page.
2.
Permission of a database item inherits from the belonging database.
3.
Permission, which is defined in code block always comes first.
Rule 1. Permission of a database is determined by the belonging page
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Usually, a database(whether it's a linked database or not) belongs to a page. And we already know how to manage permission of a page, 
Manage permission of content.
Manage permission of content.•
If a database(let's say database-A) belongs to page-1, the permission of a database-A is that of page-1.
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If a database does not belongs to any page(it could be when it's at the top hierarchy), the permission of a database comes from default permission. You can set default permission in the admin.
Rule 2. Permission of a database item inherits from the belonging database.
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If a database item belongs to database-A, then the permission of a database item is the same as database-A (Except rule 3)
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The permission of a database which is inherited to a database item is the permission of a original database, not a linked database.
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It's because a database item belongs to the original database. The permission of the database item should not be affected where user comes from. (from the original database, or some linked databases)
Rule 3. Permission, which is defined in code block always comes first.
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If a page, whether it's a database item or not, has a code block with permission key, the permission of a code block always works first.