Depending on the specific wiki engine, the presence of Php Language, My Sql, etc. may be required. Many are implemented as Common Gateway Interface (CGI) programs, so you only need the web server. Of course, if the engine is written in a language that requires a runtime component, like Perl Language, Python Language, or Java Language, you'll need that environment as well.
Other engines are, indeed, written to use additional frameworks, like PHP and Zope Application Server, and additional components like a database. Check the documentation of the particular engine for details.
See also Wiki Server
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