FALCON FLT CREW ENCOUNTERED TCAS RA DURING DESCENT AFTER SETTING INCORRECT ALT IN ALT ALERT WINDOW.

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PROCEEDING INBOUND ON THE ARR IN VMC. APPROX 40 MI E OF PVD I MENTIONED TO THE FO (WHO WAS FLYING FROM THE L SEAT) 'CTR NEEDS TO GET US DOWN TO 11000 FT; IF WE ARE TO MAKE PVD AT 11000 FT.' THE CTLR WAS BUSY; SO I DIDN'T INTERRUPT. FINALLY THE CTLR ASKED US IF HE HAD 'GIVEN US 11000 FT AT PVD.' I REPLIED 'NEGATIVE THIS IS THE FIRST MENTION OF THAT.' THE ZBW CTLR APOLOGIZED FOR THE LATE DSCNT AND CLRED US TO CROSS 5 MI E OF PVD AT 11000 FT INSTEAD OF 11000 FT. TO THE BEST OF MY KNOWLEDGE I SET 11000 FT IN THE ALT ALERT DEVICE; AND WE BOTH SAID '11000 SEEN.' HOWEVER; AFTER PASSING 10000 FT WE BOTH SAW 6000 SET IN THE ALERTER. I DON'T KNOW HOW 6000 WAS SET; NOR DO I RECALL SETTING SUCH A NUMBER IN THE ALERTER. THE ONLY 'SIX' IN OUR CLRNC WAS 'ALTIMETER OF 30.06.' THE ONLY POSSIBILITY THAT I CAN THINK OF; IS THAT SOMEHOW; IN THE HASTE TO ACCOMMODATE THE LATE DSCNT NOTICE; POSSIBLY I TRANSPOSED THE 30.06 INTO THE 6 IN THE ALT ALERTER. DURING THE DSCNT IT WAS NECESSARY TO ATTAIN 4000 FPM IN ORDER TO MEET THE NOW IMPOSED RESTR. AIRBRAKE ONE POS WAS USED. I MENTIONED TO THE FO THAT 'IT WOULD NOT BE NECESSARY TO SLOW TO 250 KIAS BY PVD SINCE THAT RESTR WAS NOT ISSUED.' SHORTLY BEFORE THAT I SAW THE 6000 FT IN THE ALT ALERT DEVICE. PASSING THROUGH 10000 FT WE GOT AN 'RA' WITH THE TFC IN SIGHT; WHEN THE CTLR QUERIED OUR ALT; THEN CLRED US TO 9000 FT WE THEN CONTINUED TO BOSTON LOGAN UNEVENTFULLY. I ACCEPT FULL RESPONSIBILITY FOR ALL ACTIONS. IN RETROSPECT; I BELIEVE THAT I ERRED IN JUDGEMENT; MOST LIKELY DUE TO FATIGUE. THE FOLLOWING APPLIES: I WAS ABLE TO SLEEP ONLY ABOUT 4-4.5 HRS LAST NIGHT. NORMALLY I SLEEP ABOUT 8 HRS PER NIGHT. ON THIS NIGHT WE HAD THE MINIMUM LEGAL REST. I IMMEDIATELY WENT TO MY HOTEL ROOM TO GET SLEEP. UPON ARRIVING AT MY ROOM I DISCOVERED THAT THE ROOM'S OUTSIDE DOOR CONNECTING TO A COMMON OUTDOOR DECK WOULD NOT LOCK OR CLOSE. SINCE ANYONE HAD ACCESS TO THE AREA; I FELT UNSAFE TRYING TO SLEEP WITH THE PEDESTRIAN TFC NEARBY WITH THE WIND BLOWING THE DOOR OPEN. THEREFORE; I ASKED FOR ANOTHER ROOM; WHICH TOOK ABOUT 45 MINS TO ARRANGE. UNFORTUNATELY THE ONLY REPLACEMENT ROOM WAS NEAR AN ELEVATOR ON THE THIRD FLOOR. THIS ELEVATOR WAS IN USE FREQUENTLY THROUGHOUT THE NIGHT WITH NOISY TOURISTS; PASSING IN AND ABOUT; WHO REPEATEDLY WOKE ME UP. THE NEXT DAY; I DID NOT REALIZE MY FATIGUE STATE. IN THE FUTURE; I SHOULD DECLINE THE TRIP SHOULD SUCH A LACK OF SLEEP OCCUR.