After reading the back and forth here I thought it was worth throwing something out here....
All the posts with quoted/cited material on the RLA mediation process, have left out a critical point.
After a PEB is called and issues a report, it isn't just "the company can impose, and the union engage self help"
The third (and most likely IMHO) possibility is that congress will act.
From nmb.gov
Under Section 10 of the RLA, if a dispute substantially threatens essential transportation in any section of the country, the NMB notifies the President who may establish a Presidential Emergency Board (PEB). If so created, the PEB has 30 days in which to investigate the dispute and report to the President during which the status-quo remains in effect. The parties may choose to accept the recommendations of the PEB, negotiate their own agreement, or, after 30 days from the issuance of the PEB report to the President exercise Self Help, unless Congress takes action.
While no airline/union dispute has risen to the level of congressional action thus far, several railroads have indeed had their disputes resolved by congress, and as AA is the nations largest carrier, it is a VERY real possibility that you guys may become the first Airline to have your contract settled by congress should mediation prove futile.