McENTEE, Circuit Judge.

This appeal involves the arbitrability of a claim for materials on a subcontract between a supplier and the principal contractor and its surety on a Massachusetts public construction project. On October 27, 1967, the defendant, Gevyn Construction Corporation, entered into a written contract with the County of Middlesex for the construction of a new County Superior Court House in the City of Cambridge. Pursuant to the contract and as required by state law, a bond was executed by Gevyn as principal and the codefendant, Travelers Indemnity Company, as surety to secure payment for all labor and materials furnished in the construction. On January 12, 1968, Gevyn entered into a subcontract with Pioneer Industries under which the latter agreed for a subcontract price of $98,300 to furnish certain materials required on the project. Pioneer alleges that it has completed its subcontract with Gevyn, has furnished certain extras and that after deducting all payments and credits there remains due from Gevyn a balance of $59,787.36, plus interest for which Pioneer demanded payment but which Gevyn has refused to pay.

During the course of construction a dispute arose between the County and Gevyn concerning the performance of the principal contract, and as a result, the County terminated the contract on May 29, 1970. About the same time Gevyn instituted an arbitration proceeding against the County to resolve certain controversies relating to so-called “foundation remedial work.” Pioneer, along with a number of other subcontractors, is a party to this arbitration and asserted a claim for $10,341. This claim is not related, however, to the instant case. Subsequently, Gevyn commenced a second arbitration proceeding against the County asserting a claim for wrongful termination of the principal contract. The record indicates that included in this second arbitration proceeding is a claim for all work performed and/or damages incurred by Gevyn, including claims by Pioneer and other affected subcontractors and suppliers. Gevyn contends that the termination arbitration will be determinative of Pioneer’s claim against it as well as those of the other subcontractors and suppliers. 1 Pioneer, however, is not a party to the second arbitration proceeding and has not asserted any claim therein. On the contrary, it filed a timely sworn statement of its claim with the Middlesex County Treasurer and brought this suit to enforce a statutory right of payment against Gevyn and its surety, Travelers, under Mass.Gen.Laws ch. 149, § 29 (1971). After removing the case to the district court on diversity grounds Gevyn and Travelers filed motions under the Federal Arbitration Act for an order staying the suit and directing Pioneer to *584 proceed with arbitration. The district court denied both motions and this appeal followed. 2

As indicated above, the principal issue on appeal is whether Pioneer is contractually required to arbitrate its claim against Gevyn or whether it is entitled to proceed with the instant suit and reduce its claim to judgment. Since it is well settled that arbitration is a matter of agreement between the parties, the question here is whether Pioneer agreed, under any reasonable construction of its subcontract with Gevyn to arbitrate the instant dispute. See United Steelworkers of America v. American Mfg. Co,, 363 U.S. 564, 80 S.Ct. 1343, 4 L.Ed.2d 1403 (1960); United Steelworkers of America v. Warrior & Gulf Navigation Co., 363 U.S. 574, 80 S.Ct. 1347, 4 L.Ed.2d 1409 (1960); United Steelworkers of America v. Enterprise Wheel & Car Corp., 363 U.S. 593, 80 S.Ct. 1358, 4 L.Ed.2d 1424 (1960).

Initially we assume, as defendants vigorously argue, that the broad arbitration provision of the principal contract is incorporated by reference into the subcontract. However, Section 1 of the subcontract states, “In the event of any conflict between the provisions of this contract and of the Principal Contract the provisions of this contract shall control.” Therefore the question here is whether any provision of the subcontract is applicable to arbitrability of this dispute. Section 18 of the subcontract provides as follows:

“Any dispute or claim between the parties arising out of this Contract or any termination thereof by the Contractor shall be submitted to a Court of Competent Jurisdiction by either party if $3500.00 or more is involved. Should such dispute or claim be in an amount under $3500.00, then the parties hereto agree to arbitrate such dispute in accordance with the rules of the American Arbitration Association then obtaining.”

Since Pioneer’s claim exceeds $3500, this section is squarely applicable and arbitration is not required. Defendants contend that § 18 does not cover Pioneer’s claim because it arises out of the termination of the principal contract by the owner and thus is not a claim arising out of the subcontract or its termination by the contractor within the meaning of § 18. The defendants read this section too narrowly. The phraseology “any dispute or claim . . . arising out of this contract” includes the instant dispute, and we cannot see that the phrase “or any termination thereof by the Contractor” in any way limits the generality of the “any dispute” language.

Nor do we think that § 19 in any way alters the situation. 3 Arguably § 19 *585 limits the defendants’ liability to Pioneer to the amount paid by the Owner. It does not, however, expressly or impliedly require that such amount be determined in an arbitration proceeding. In the absence of an agreement to the contrary, a claim to which § 19 may apply and which involves interpretation of that section falls within the ambit of § 18 because it is, ipso facto, a dispute arising out of the subcontract.

The defendants further argue that since § 19 limits the extent of Pioneer’s recovery to the amount received by Gevyn from the County, a stay is appropriate to avoid inconsistent results between this ease and the termination arbitration proceeding. 4 If they are correct, Pioneer’s success in this action would rise or fall with Gevyn’s success in the termination arbitration, and should Gevyn recover nothing in the arbitration, it would be exonerated here. Such a result directly contravenes the legislative objective underlying ch. 149, § 29, a statute which the parties concede is applicable here. In American Air Filter Co., Inc. v. Innamorati Bros., Inc., Mass., 260 N.E.2d 718 (1970), the Supreme Judicial Court found that a contractor’s surety was liable to one who supplied heating equipment to a heating subcontractor despite the intervening bankruptcy of the subcontractor and his nonperformance. In view of the broad construction given to the statute in that and other cases, we are convinced that a Massachusetts court would refuse to allow the parties to defeat such a strong remedial statute by private agreement. We hold, therefore, that any provision in the instant subcontract purporting to limit Pioneer’s recovery to a portion of Gevyn’s recovery from the County is unenforceable.

Since Pioneer has not agreed to arbitrate this dispute and since the defendants are not entitled to a stay as a matter of equity, the order of the district court is affirmed.

Notes

. These two arbitration proceedings have been consolidated and are still pending.

. The district court’s denial of Gevyn’s petition under 9 U.S.C. § 4 for an order directing Pioneer to proceed to arbitration is appealable as a “final” order pursuant to 28 U.S.C. § 1291. See County of Middlesex v. Gevyn Const. Corp., 450 F.2d 53 (1st Cir. 1971); New England Power Co. v. Asiatic Petroleum Corp., 456 F.2d 183 (1st Cir. 1972) (dictum); 9 Moore’s Federal Practice ¶ 110.20 [4.-1] (1), at 246-47 (2d ed. 1970).

. Section 19 of the subcontract provides as follows:

“In the event the Owner terminates or cancels the Principal Contract for any cause whatsoever at any time after tiie date hereof, this contract shall likewise be deemed cancelled and terminated and, it is understood that the Supplier shall have no claim of any kind whatsoever against the Contractor for breach of this contract or for any cause or reason whatsoever. The Contractor shall be under no liability to the Supplier therefor, except that the Contractor shall be liable to the Supplier only for the difference between the contract value of the labor and materials furnished to the date of said termination or cancellation of the Principal Contract in so far as said labor and materials have been accepted, approved and paid for by the Owner, and the amount theretofore paid on account of said Contract by the Contractor to the Supplier. It is understood that the Contractor has the same power as regards terminating this contract that the Owner may exercise over the Contractor under any provision of the *585 Principal Contract in addition to any and all such, powers to terminate contained herein.”

. Section 11B of the subcontract has a similar limiting provision:

“[I]t being expressly understood and agreed, anything in this Subdivision ‘B’ to the contrary notwithstanding, that the liability, if any, of the Contractor to the Supplier shall be payable only out of funds, if any, received by the Contractor from the Owner on account of any such claim. The Supplier hereby agrees to accept as final the determinations of the Owner with respect to any such claims.”