GULF 4 CREW HAD A TCASII TA WITH AN ACFT ON THE SKEBR 1 RNAV ARR AT LAS.

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WE HAD TAKEN OFF FROM LAX AND HAD STARTED OUR DSCNT INTO LAS (CLRED FOR THE SKEBR RNAV 1 ARR). AT 13000 FT MSL AND PAST SKEBR INTXN; ATC CLAIMS TO HAVE ISSUED A CLRNC TO 'SLOW TO 220 KTS THEN DSND TO 12000 FT MSL.' I THEN READ BACK 'WE WILL SLOW TO 220 KTS THEN DSND TO 11000 FT MSL.' NOTE: JUST PRIOR TO HAVING READ BACK THIS CLRNC; I HAD FINISHED COMMUNICATING WITH THE FBO AT OUR DEST ON #2 RADIO; WHILE THE CAPT WAS MONITORING/COMMUNICATING ON THE #1 FREQ (ATC). HOWEVER; ATC DID NOT ACKNOWLEDGE OR CORRECT MY READBACK OF THE CLRNC. AS WE WERE CONTINUING OUR DSCNT FROM 13000 FT MSL AND AT APPROX 12000 FT MSL; I NOTICED A BLUE ADVISORY TARGET ON OUR TCASII DISPLAY (APPROX 4-5 NM AWAY). WHILE TAKING A FEW SECONDS TO FIND THIS TARGET VISUALLY; I FELT THAT WE MIGHT NEED TO COMMUNICATE THIS INFO TO ATC (AS I DO NOT REMEMBER ATC ADVISING US OF THIS TFC/TARGET). I ASKED ATC 'WE HAVE TFC AT OUR 2 O'CLOCK POS; CONFIRM YOU WANT US TO DSND TO 11000 FT MSL.' WHILE WE WERE WAITING FOR ATC'S RESPONSE; THE CAPT REDUCED HIS RATE OF DSCNT; AND MOMENTARILY LEVELED THE ACFT AT APPROX 11550 FT MSL SO AS TO MINIMIZE ANY FURTHER CONFLICT WITH THE APCHING TARGET. AFTER A LONGER THAN NORMAL DELAY IN REPLY; ATC RESPONDED THAT SHE HAD CLRED US TO DSND AND MAINTAIN 12000 FT NOT 11000 FT MSL. THE CAPT THEN STATED THAT WE (FO) HAD READ BACK 11000 FT MSL AND THAT SHE DID NOT ACKNOWLEDGE OR CORRECT OUR READBACK. IT WAS THEN THAT THE CAPT INITIATED A GENTLE CLB BACK TO 12000 FT MSL. WE THEN SUCCESSFULLY COMPLETED THE ARR; VISUAL APCH; AND LNDG WITHOUT INCIDENT. AFTER LNDG; I REMAINED IN THE ACFT TO COMPLETE MY DUTIES WHILE THE CAPT WENT INSIDE TO DISCUSS WHAT HAD TRANSPIRED WITH THE APPROPRIATE ATC PERSONNEL. UPON HIS RETURN; THE CAPT STATED THAT HE HAD TALKED AT LENGTH WITH SUPVR; AND HAD A CONFERENCE CALL WITH BOTH DIRECTOR OF AVIATION AND PROGRAM MGR. THE CAPT VERBALLY COMMUNICATED THE FOLLOWING HIGHLIGHTS OF HIS CONVERSATION WITH SUPVR: 1) SUPVR STATED THAT THE FO DID INDEED REPLY WITH 'SLOW TO 220 KTS; THEN DSND TO 11000 FT MSL.' 2) SUPVR ALSO STATED 'ATC DID NOT ACKNOWLEDGE OR CORRECT OUR ALT READBACK ERROR.' I FEEL THAT OUR EFFORTS TO MAINTAIN A VIGILANT WATCH FOR OTHER ACFT AND THE CORRECTIONS WE BEGAN MAKING BEFORE ATC HAD ADVISED US OF THE OTHER ACFT; DURING THE LONG PAUSE OF VERIFICATION OF THE CLRNC FROM ATC; AND AFTER WE WERE ASKED TO CLB TO 12000 FT MSL ALL MADE IT POSSIBLE FOR US TO 'SEE AND AVOID' AND MINIMIZE ANY CONFLICT BTWN US AND THE OTHER ACFT.