In a recent issue of New Scientist (16 Aug 2010), I was surprised to read that a part of Wiles' proof of Taniyama-Shimura conjecture relies on inaccessible cardinals.

Here's the article

* Richard Elwes, _[To infinity and beyond: The struggle to save arithmetic](https://www.newscientist.com/article/mg20727731-300-to-infinity-and-beyond-the-struggle-to-save-arithmetic/)_, New Scientist, August 2010.

Here's the relevant bit from the article:

>"Large cardinals have been studied by logicians for a century, but their intangibility means they have seldom featured in mainstream mathematics. A notable exception is the most celebrated result of recent years, the proof of Fermat's last theorem by the British mathematician Andrew Wiles in 1994 [...] 
To complete his proof, Wiles assumed the existence of a type of large cardinal known as an inaccessible cardinal, technically overstepping the bounds of conventional arithmetic"

Is this true ?
If so, could someone please outline how they are used ?