POTENTIAL LOSS OF SEPARATION BETWEEN CORP ACFT AND TRAILING ACR CLIMBING TO SAME ASSIGNED ALT. OPERATIONAL DEVIATION.

Narrative

ATC HAD CLRED US TO CLB TO 12000' MSL. COPLT READ BACK 12000'. PLT CLBED TO 12000'. AT 11700' ATC SAID HE HAD CLRED US TO 10000'; LEFT US AT 12000' WHILE CHKING THE SCOPE. ATC THEN CLRED US TO 10000' WITH EXPEDITED DSCNT. WE WERE INFORMED THAT AN ACR WAS CLBING THROUGH 11700'; 4 MI IN TRAIL OF US. WE LEVELED AT 10000' WITHIN 2 MINS. COPLT ASKED ATC IF WE HAD SET OFF ANY ALARMS. ATC SAID NEGATIVE. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING: WENT OVER SEQUENCE OF EVENTS WITH RPTR TO TRY TO ASCERTAIN FOR SURE IF THE ATC JURISDICTION WAS ZAU OR ORD DEP CTL. EXPLAINED THAT ZAU WOULD NEED 5 MI SEP; BUT DEP CTLR WOULD ONLY NEED 3 MI TO BE LEGAL. AFTER OUR DISCUSSION THE RPTR DECIDED THAT THEY WERE STILL WITH DEP CTLR AND WERE CHANGED TO ZAU AFTER GETTING BACK DOWN TO 10000'. I ADVISED HIM I WOULD REFLECT THE CHANGE IN HIS RPT. HE HAS HAD NO FURTHER FOLLOW UP FROM FAA. WE TALKED ABOUT THE HEARBACK PROB IN ATC; AND HE SAID THAT HE HEARS MANY PLTS AND CTLRS WHO DO NOT SEEM TO USE PROPER RADIO PROC AND PHRASEOLOGIES.