859 So.2d 1271 (2003)

REUTER RECYCLING OF FLORIDA, INC., a Florida corporation, Appellant,
v.
CITY OF DANIA BEACH; City of Hallandale Beach; City of Pembroke Pines; and City of Pompano Beach, Appellees.

No. 4D03-386.

District Court of Appeal of Florida, Fourth District.

November 26, 2003.

*1272 Jeffrey S. Wertman, Mitchell W. Berger and David L. Ferguson of Berger, Singerman, Fort Lauderdale, for appellant.

Jennifer A. Goldberg and Michael S. Popok of Weiss, Serota, Helfman, Pastoriza, Guedes, Cole and Boniske, P.A., Fort Lauderdale, for appellees.

FARMER, C.J.

We reverse a trial judge's order refusing to enjoin binding arbitration. The claims sought to be arbitrated are excluded by the arbitration agreement. Thus Reuter is irreparably harmed by the trial court's refusal to enjoin arbitration of claims not included in an agreement to arbitrate. See K.W. Brown & Co. v. McCutchen, 819 So.2d 977, 979 (Fla. 4th DCA 2002) ("A legal remedy is inadequate in this case, as no legal remedy can compensate... for having to allegedly undergo an arbitration process in which they did not agree to participate. In the absence of *1273 injunctive relief, [a party] would be forced to proceed with an arbitration proceeding to which they did not ... consent."). With arbitration agreements, the rule is effectually that the presumptive remedy is specific performance, regardless of whether the ultimate decision is for or against arbitration of the claim in issue.

Reuter established that the subject agreement to arbitrate did not include claims barred by the applicable statute of limitations. The contract states:

"All claims, disputes and other matters in question arising out of, or relating to, this Agreement or the breach thereof, shall be decided by arbitration.... The demand for arbitration shall be made within a reasonable time after the claim, dispute or other matter in question has arisen, and in no event shall it be made when institution of legal or equitable proceedings based on such claim, dispute or other matter in question would be barred by the applicable statute of limitations."

We do not find this provision ambiguous. It expressly excludes time-barred claims from the agreement to arbitrate.

Even if the agreement to arbitrate were ambiguous, we would still find that the parties had not agreed to have the arbitrators determine the issue of arbitrability. As we said in Corporate Securities Group Ltd. v. Lind, 753 So.2d 151 (Fla. 4th DCA 2000), where we construed the functionally identical federal arbitration statute:

"the question whether the arbitrators or the courts have the primary power to determine arbitrability depends on whether the parties agreed to submit the question of arbitrability itself to arbitration." 753 So.2d at 152. We now make clear that the same rule applies to agreements covered by the Florida Arbitration Code.

The rule is that "courts should not assume that the parties agreed to arbitrate arbitrability unless there is `clea[r] and unmistakabl[e]' evidence that they did so." Lind, 753 So.2d at 152 (quoting First Options of Chicago v. Kaplan, 514 U.S. 938, 944, 115 S.Ct. 1920, 131 L.Ed.2d 985 (1995)). An ambiguity as to who should determine arbitrability means that the parties have not clearly and unmistakably manifested an intent to have arbitrators decide the issue as to what specific claims they have agreed to arbitrate. Thus if the agreement is ambiguous, then it is for the court to say what claims should be arbitrated. Lind, 753 So.2d at 152. We hold that in this instance the trial court erred in finding that the parties had clearly and unmistakably agreed to have the arbitrators determine arbitrability as to time-barred claims.

REVERSED.

GUNTHER and MAY, JJ., concur.

REUTER RECYCLING OF FLORIDA, INC., a Florida corporation, Appellant, v. CITY OF DANIA BEACH; City of Hallandale Beach; City of Pembroke Pines; and City of Pompano Beach, Appellees.

REUTER RECYCLING OF FLORIDA, INC., a Florida corporation, Appellant,
v.
CITY OF DANIA BEACH; City of Hallandale Beach; City of Pembroke Pines; and City of Pompano Beach, Appellees.