A B737 WAS DISPATCHED IN NON COMPLIANCE WITH THE ENTIRE PRESSURIZATION SYS DEFERRED AS INOP BUT NOT PLACARDED PER THE MEL.

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ON DSCNT FROM FL350; WE GOT AN ALT ALERT HORN INDICATING THE CABIN ALT WAS AT 10000 FT. WE FOLLOWED THE PROPER PROCS AND DECLARED AN EMER. PASSING FL310 IN OUR DSCNT; WE REGAINED CTL OF THE CABIN ALT; CANCELED THE EMER; AND LANDED UNEVENTFULLY. WE NOTIFIED OUR MAINT CTLR OF THE PROB IN THE AIR AND ON THE GND IN ZZZ. SINCE WE DIDN'T HAVE OUR OWN MAINT PERSONNEL IN ZZZ; WE WERE MET BY CONTRACT MAINT. AFTER TALKING WITH OUR MAINT CTLR; HE NOTIFIED US THAT HE HAD FOUND WHAT HE THOUGHT WAS THE PROB -- A SEAL AROUND THE AFT ENTRY DOOR. IT WAS OUR UNDERSTANDING HE WAS DOING TO THEN CLR THAT MAINT ITEM. ABOUT 15 MINS LATER; THE CONTRACT MAINT PERSONNEL RETURNED AND GAVE THE CAPT THE LOGBOOK. HE NEVER SAID A WORD AND DID NOT GIVE US ANY STICKER TO PUT ON ANY DEFERRED ITEM. I SAW THE CAPT LOOK AT THE LOGBOOK; THEN SAY 'IT LOOKS OK' AND GAVE THE RELEASE TO THE AGENT. UPON REACHING FL210 IN CRUISE; I GOT THE LOGBOOK TO SEE WHAT THE MAINT PERSONNEL HAD DONE AND DISCOVERED THEY HAD DEFERRED THE ENTIRE PRESSURIZATION SYS. WE WERE USING THAT PRESSURIZATION SYS IN THE AUTO MODE AT THE TIME. I BROUGHT THIS TO THE CAPT'S ATTN. HE THEN CALLED THE DISPATCHER AND HAD THE MEL NUMBER CHANGED TO ALLOW US TO USE THE SYS IN THE MANUAL MODE. I ASKED HIM IF HE WANTED ME TO OPERATE THE PRESSURIZATION IN MANUAL AND HE SAID 'NO' AS IT APPEARED TO BE WORKING NORMALLY.