MediaWiki is the software Consumerium uses on its R&D wiki which you are using right now. It is one of several wiki code options, seemingly the one that has a wikitext standard suitable for large numbers of people to collaborate on in many languages. http://mediawiki.org
It is not however ideal as a piece of code to work with our hardware requirements or protocol requirements, e.g. it does not currently integrate with any chat code. Nor does it implement some features of the content wiki or opinion wiki that will be needed eventually to deliver Consumerium Services such as signing versions of articles, which is needed for non-centralized integrity burden of proof.
Therefore its use at present is really just a test, and to make it easier to collate text from other GFDL services, most of which also use mediawiki. Consumerium developers will have to make their choices based also on the constraints the Consumerium License might place on using GPL'd code. This might not be an issue, or it might be a huge issue, we just don't know.