With current technologies advancing in USA, they are now finishing their F-35 (Lockheed Martin Lightning II).
http://en.wikipedia.org/wiki/Lockheed_Martin_F-35_Lightning_II
there is one variant, F-35B, which consist of short take-off, and vertical landing (like a harrier).
With such variant, it is possible to make a smaller AIRCRAFT CARRIER, which is more maneuverable, travel faster, and risk being diversified, as all the F-35B's can land in other smaller ships, like landing on the Destroyer, Cruisers, Support Ships, or even modifying the Battleship, Destroyer, Cruisers, Support Ship to become Aircraft Carrier, while just carrying a few units of F-35B.
The whole point of having an Aircraft Carrier is to have AIR SUPERIORITY over AREA OF OPERATION. An Aircraft Carrier by itself provides the means to that Goal.
So, with the F-35B, this makes it possible for USA to modify their ARMADA to install short take off ramps and landing pads to Battleships, Destroyers, Cruisers, Support Ships. Making existing AIRCRAFT CARRIER redundant.
However, with all combined information as per discussed from all Military Experts, would be, or otherwise, IT IS STILL POSSIBLE to destroy AIRCRAFT CARRIERS with;
1. SATURATION of ASBM (ANTI-SHIP BALLISTIC MISSILE)
2. SATURATION of AIRCRAFT attack
3. Nuclear AIR Blast.
Leaving politics aside, EVERYTHING HAVE A WEAKNESS... NOTHING IS IMPOSSIBLE.