CAPT OF A CANADAIR CL65 OVERSHOT ASSIGNED ALT DURING DSCNT DUE TO SETTING THE ALT ALERTER TO THE WRONG ALT RESULTING IN A GPWS ALERT AND AN ATC LOW ALT ALERT.

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WE WERE IN DSCNT TO MRY ON A VECTOR TO THE ILS APCH. APCH CLRED US TO DSND TO 6000 FT. I READ BACK 6000 FT AND LOOKED OVER AT MY CHARTS. AS I WAS STUDYING MY CHARTS; THE CAPT MENTIONED THE GREAT VIEW. I LOOKED OUT AND NOTICED WE WERE LOW. THIS DID NOT CONCERN ME AS WE FLEW THIS RTE BEFORE IN VMC AND OUR ALT APPEARED NORMAL. NEXT I HEARD THE GPWS 'TERRAIN' ALERT. I THOUGHT IT TO BE MOMENTARY. NEXT THE '1000 FT TO GO' CHIME SOUNDED FOLLOWED BY CONTINUOUS GPWS ALERTS. I THEN NOTICED THE ALT PRESELECT AT 3000 FT AS WE DSNDED THROUGH 4000 FT. RADAR ALT SHOWED 1600 FT. I THEN TOLD THE CAPT 6000 FT AND HE INITIATED A CLB. APCH CAME ON WITH A LOW ALT ALERT. THE CAPT SAID HE HEARD AND SET 3000 FT. I SHOULD HAVE DOUBLECHKED THE ALT PRESELECT AS HE SET IT. CONTRIBUTING FACTORS WERE THE VERY EARLY SHOW TIME WE HAD THAT MORNING (XO00) DES MOINES TIME WHICH IS 2 HRS LATER THAN PHOENIX TIME. WE BOTH UP AT XC00 WHICH IS REALLY XA00 IN ARIZONA. AT THE TIME OF THE SIT WE HAD FLOWN 4.5 HRS AND IT WAS THE END OF A 5 DAY TRIP. WE WERE BOTH VERY TIRED. I FEEL THAT OUR MENTAL STATE WAS THE BIGGEST CONTRIBUTING FACTOR. FROM NOW ON I WILL ALWAYS FOLLOW PROPER CRM TO AVOID SIMILAR DISCREPANCIES FROM OCCURRING.