delivered the Opinion of the Court.
Bennett College, Bennett College Foundation, Inc., and Pace University (the Col*365leges) petitioned for certiorari review of the court of appeals decision in United Bank of Denver v. St. John’s Episcopal Cathedral, Nos. 87CA1050 & 87CA1051 (Colo.App. March 23, 1989) (unpublished opinion). In United Bank of Denver, the court of appeals affirmed the Denver probate court’s summary judgment entered against the Colleges. We granted certiora-ri to consider whether the court of appeals properly applied the doctrine of collateral estoppel.1 We affirm.
I.
A.
In 1970, Margaret Collbran, an alumna of Bennett College, established a trust, with the United Bank of Denver as the trustee (the Collbran Trustee), providing that upon her death the remainder of the trust would be “divided into equal parts and distributed outright to each of the following organizations” in existence at the time of her death: St. John’s Episcopal Cathedral, Dumb Friends League Animal Shelter, Metropolitan Opera Guild, Inc., and Bennett College.
In May 1977, Bennett College, an all-women’s college, filed for bankruptcy in federal district court, which adjudicated Bennett College bankrupt in October 1977. By March 1978, the bulk of Bennett College’s assets had been liquidated and disbursed to creditors. The bankruptcy estate was closed in 1984.
Following Collbran’s death on February 22, 1986, the Collbran Trustee petitioned the Denver Probate Court for instructions on whether or how it should distribute Bennett College’s interest in the trust corpus. In the probate proceedings, St. John’s Episcopal Cathedral, Dumb Friends League Animal Shelter, and Metropolitan Opera Guild (the Charities) argued that Bennett College’s interest in the trust corpus should be distributed equally among them because Bennett College is no longer in existence.2 Bennett College Foundation, Inc., (Bennett Foundation), and Bennett College, which has not received students since 1977 although the state of New York has not divested the college of its school charter, and Pace University3 argued that Bennett College was still in existence at the time of Collbran’s death.
The Charities subsequently filed two motions for sumpiary judgment against the Colleges, arguing that they were collaterally estopped and judicially estopped from asserting that Bennett College was still in existence at Collbran’s death. The motions for summary judgment were based on previous New York court cases following the adjudication of Bennett College’s bankruptcy in which the college’s entitlement to funds unrelated to the Collbran trust was questioned. The probate court granted the Charities’ motions for summary judgment, and the court of appeals affirmed.
B.
Because of the limited nature of our review in this case, see note 1, supra at 365, we consider only the New York case on which the probate court and court of appeals relied in holding that the Colleges were collaterally estopped from asserting that Bennett College was still in existence at the time of Collbran’s death.
In 1937, Margaret Gage, a New York resident and alumna of Bennett Junior Col*366lege, established a trust fund and named Bennett College as its beneficiary.4 The trust provided that another charitable beneficiary could be named “[i]n the event that [Bennett College] cease[s] to exist, whether by reason of dissolution, merger, consolidation or otherwise.” Bankers Trust Company (the Gage Trustee) eventually was named the trustee. The Gage Trustee stopped disbursing trust moneys to Bennett College in September 1977, after the college had filed for bankruptcy in May 1977.
In May 1979, the Gage Trustee initiated a proceeding in the Supreme Court of New York for, inter alia, a ruling that Bennett College had ceased to exist by virtue of the college’s bankruptcy and the subsequent sale of its assets, and that the Gage Trustee was no longer obligated to disburse trust moneys to Bennett College. Notice of the proceeding was served on Bennett College through the college’s last president, J.W. Nystrom, the bankruptcy trustee for Bennett College (the Bankruptcy Trustee), and the New York Attorney General.5
In July 1979, the Gage Trustee, the Bankruptcy Trustee, and apparently the New York Attorney General entered into a stipulation by which the Gage Trustee agreed to pay $3,668.22 to the Bankruptcy Trustee.6 The amount represented the net moneys that were payable to Bennett College but had not been paid because of the Gage Trustee’s concern over whether the college continued to exist as required by the Gage trust. Also in July 1979, the Supreme Court of New York issued a memorandum decision finding that Bennett College had “ceased to exist” and permitting the Gage Trustee to substitute other beneficiaries to the Gage trust in accordance with the trust’s terms.
In September 1979, the Supreme Court of New York approved the July 1979 stipulation, and, after referring to its July 1979 memorandum decision, “ORDERED, ADJUDGED AND DECREED that Bennett College ... has for the purposes of [the Gage] Trust ceased to exist.” „
II.
The Colleges argue that the court of appeals and probate court erroneously applied the doctrine of collateral estoppel in this case. We disagree.
Collateral estoppel, or issue preclusion, bars relitigation of an issue that was determined at a prior proceeding if: (1) the issue precluded is identical to an issue actually determined in the prior proceeding; (2) the party against whom estoppel is sought was a party to or was in privity with a party to a prior proceeding; (3) there was a final judgment on the merits in the prior proceeding; and (4) the party against whom the doctrine is asserted had a full and fair opportunity to litigate the issue in the prior proceeding. E.g., City of Colorado Springs v. Industrial Comm’n, 749 P.2d 412, 414 (Colo.1988); Industrial Comm’n v. Moffat County School Dist. RE No. 1, 732 P.2d 616, 619-20 (Colo.1987); United States v. Jesse, 744 P.2d 491, 503-04 (Colo.1987). The issue on which preclusion is asserted must have been actually litigated and necessarily adjudicated in the prior proceeding. Jesse, 744 P.2d at 503.
A.
We first consider whether the issue of Bennett College’s existence that was decided in the New York proceeding is identical to the issue before the Denver Probate Court.
*367The Gage trust provided that another charitable beneficiary could be named “[i]n the event that [Bennett College] cease[s] to exist, whether by reason of dissolution, merger, consolidation or otherwise.” In its “Petition for Voluntary Accounting and Construction of Deed of Trust,” the Gage Trustee specifically requested that the New York Supreme Court determine “for purposes of the administration of said trust [that] Bennett College ... ceased to exist on or about August 8, 1977.”
The Collbran trust provided that upon Collbran’s death the trust would be “divided into equal parts and distributed outright to the [named] organizations that are in existence” at the time of her death. In its “Petition for Order Ascertaining Beneficiaries of Trust,” the Collbran Trustee stated that the Charities had requested distribution of the trust corpus to the Charities only, because Bennett College was not in existence at the time of Collbran’s death. The Collbran Trustee also stated in the petition that it was “uncertain” whether it was required to distribute a one-fourth share to Bennett College because, inter alia, the Gage Trustee had learned that Bennett College had been adjudicated a bankrupt, that the college had not conducted classes or functioned as an academic institution since fall 1977, and that in the Gage trust court proceedings the New York Supreme Court had found that, for purposes of the Gage Trust, the college had ceased to exist. The Collbran Trustee requested through the petition that the Denver Probate Court determine the beneficiaries of the trust and instruct the Coll-bran Trustee on how to distribute the trust assets to the beneficiaries.
The Colleges argue that the issues in the two court proceedings are different because “[e]ach trust is unique, which requires that each be examined independently.” Specifically, the Colleges argue that the issue in the Gage trust court proceeding must have involved a different issue because the document creating the Gage trust defined cessation of existence as “dissolution, merger, consolidation or otherwise,” and the document governing the Collbran trust does not define “existence.” We disagree.
A comparison of the facts in the Gage trust court proceedings and the court proceedings in this case demonstrates that the issue before the New York Supreme Court was identical to the issue before the Denver Probate Court: whether or not Bennett College was in existence. The Gage trust deed’s definition of “exist” did not cause the issue in the New York court proceedings to be different from the issue before the Denver Probate Court. The deed’s definition of “exist” — “dissolution, merger, consolidation or otherwise” — is too broad to differentiate the Gage trust deed’s use of “exist” from the Collbran trust instrument’s use of “existence.” Cf Webster’s Third International Dictionary 796 (1986) (“exist” means “to have actual or real being” or to “have being in space and time”).
B.
The Charities argue, and the probate court and court of appeals held, that the Colleges were in privity with Bennett College’s bankruptcy trustee during the 1977-1978 bankruptcy proceedings of the college. We agree.
For purposes of collateral estoppel, a privy is one who, after rendition of judgment, has acquired an interest in the subject matter affected by the judgment through or under one of the parties, as by successor, inheritance, or purchase. See Murphy v. Northern Colorado Grain Co., 30 Colo.App. 21, 24, 488 P.2d 103, 104 (1971) (citing Bernhard v. Bank of America Nat’l Trust & Sav. Ass’n, 19 Cal.2d 807, 810, 122 P.2d 892, 894 (1942)), cited with approval in Pomeroy v. Waitkus, 183 Colo. 344, 350, 517 P.2d 396, 399 (1973).
The bankruptcy trustee is considered to be the successor in interest to the debtor and the debtor’s property during the bankruptcy proceeding, IB J. Moore, J. Lucas & T. Currier, Moore’s Federal Practice ¶ 419[3.-1], at 634 (2d ed.1988) [hereinafter IB Moore’s Federal Practice], to collect, liquidate, and ultimately distribute the trustee’s estate to the creditors. Bank*368ruptcy Act of 1898, ch. 541, 30 Stat. 544, 557 [hereinafter Bankruptcy. Act] (1978 repeal effective 1979), 1979 version reprinted, in 11 U.S.C.A.App. at 141, 180-81 (West 1979) (current version at 11 U.S.C. §§ 101 to 1330 (1979 and Supp.1990)).7 Although under the Bankruptcy Act a trustee is considered a representative of the creditors, the trustee for many purposes is deemed to be in privity with the debtor and stands in the debtor’s shoes. 2 D. Cowans, Bankruptcy Law and Practice § 604 (2d ed. 1978); accord In re Ahead By A Length, Inc., 100 B.R. 157, 173 (Bankr.S.D.N.Y.1989); see also Heiser v. Woodruff, 327 U.S. 726, 734, 66 S.Ct. 853, 857, 90 L.Ed. 970 (1946) (holding that issue of fraud litigated between creditor and bankrupt, and litigated between creditor and bankruptcy trustee, “who represents the bankrupt and [the bankrupt’s] creditors,” is res judicata and cannot be further litigated in the bankruptcy proceeding); 4 Collier on Bankruptcy ¶ 704.02 n. 2 (L. King 15th ed. 1979) (“Rights of action arising upon the contracts or property of the debtor, not yet resolved into suit, pass to the trustee, and [the trustee] should assert them in the proper tribunal whenever necessary for the collection or preservation of the estate.”) (citing In re Bowling Green Milling Co., 36 F.Supp. 785, 786 (W.D.Ky.1941)).8
For purposes of the application of collateral estoppel on the issue of whether Bennett College was in existence at the time of Collbran’s death, we conclude that the Bankruptcy Trustee was a privy to Bennett College.
C.
The Colleges argue that the third requirement for the application of collateral estoppel — final judgment on the merits in the prior proceeding — cannot be satisfied in this case, because the issue of Bennett College’s existence was not actually and necessarily decided by the New York Supreme Court in the Gage trust court proceedings because the parties reached a settlement.
Under certain circumstances a stipulation between parties to central questions of fact and law or a stipulation to questions of fact may render a judgment not “final” as to those questions, and in a subsequent proceeding collateral estoppel should not prevent the litigation of those questions unless the parties in the original lawsuit intended the questions to be settled as to future actions. See Restatement (Second) Judgments § 27 comment e (1980); 1B Moore’s Federal Practice ¶ 0.444[4].
In this case, the “stipulated fact” doctrine is inapplicable. Because the trustee for the Gage trust placed in issue — through its petition for accounting and construction of deed of trust — Bennett College’s existence, and because the issue of the college’s existence was crucial to the trustee’s decision on how it would disburse the trust corpus, the New York Supreme Court could not avoid entering an order deciding the issue.
The question, then, is whether the parties to the Gage trust proceedings reached a stipulation of fact on the question of Bennett College’s existence. We conclude that the parties did not reach such a stipulation. The New York Supreme Court order indicates that the parties to the Gage trust proceedings stipulated only to the amount owed and payable to Bennett College during the period from September 6, 1977, to October 14, 1977.9 Additional evi*369dence indicating that the parties had not reached a stipulation on the question of Bennett College’s existence is that the parties’ July 13, 1979, stipulation was preceded by the New York Supreme Court’s July 2, 1979, “Memorandum Decision,” which provided in relevant part:
Upon the foregoing papers there being no objection, this application to settle trustee’s account and for a construction granting petitioner permission to substitute as beneficiary in place and stead of Bennett College, which has ceased to exist, ... one or more ... organizations ... is granted.
(Emphasis supplied). The New York court’s “Final Judgment on Intermediate Accounting” incorporated the Memorandum Decision, and “ORDERED, ADJUDGED AND DECREED that Bennett College ... has for the purposes of said Trust ceased to exist.”
We hold that the 1979 stipulation does not prevent the application of collateral es-toppel to the issue of Bennett College’s existence.
D.
The Colleges’ final argument is that they were deprived of a full and fair opportunity to litigate Bennett College’s existence in the Gage trust proceeding.10 We disagree.
As we have stated, the Bankruptcy Trustee was in privity with Bennett College, and the Bankruptcy Trustee is under a fiduciary duty to preserve the debtor’s estate. See 2 D. Cowans, supra p. 11, § 604; see also 4 Collier on Bankruptcy, supra p. 11, 11704.02 n. 2. Thus the issue we must resolve is whether the Bankruptcy Trustee was given a full and fair opportunity to litigate the issue of Bennett College’s existence in the Gage trust proceeding.
Factors determinative of whether a party has been given full and fair opportunity to litigate include whether the remedies and procedures in the first proceeding, or the proceeding itself, is substantially different from the proceeding in which collateral es-toppel is asserted, see Salida School Dist. R-32-J v. Morrison, 732 P.2d 1160, 1164 (Colo.1987); whether the party in privity in the first proceeding has sufficient incentive to vigorously assert or defend the position of the party against which collateral estop-pel is asserted, see id.; and the extent to which the issues are identical, 18 C. Wright, A. Miller & E. Cooper, Federal Practice and Procedure § 4423, at 221 (1981). See generally Wright, Miller & Cooper, supra, § 4423.
Applying these factors, we can find nothing in the record suggesting that the Colleges were denied a full and fair opportunity to litigate through the Bankruptcy Trustee. The New York Supreme Court proceedings were substantially similar, and the Colleges have not argued that the New York trial procedures are substantially different from Colorado’s trial procedures. With more than $465,000 at stake in the trust corpus, we conclude that the Bankruptcy Trustee, who was obligated to preserve Bennett’s College’s assets, had adequate incentives to assert in the New York court the existence of Bennett College. Finally, the issue in the Gage trust proceedings and the issue in the Collbran trust proceedings were identical.
III.
We hold that the probate court and court of appeals properly applied the doctrine of collateral estoppel on the issue of Bennett College’s existence.
Judgment affirmed.
Justice LOHR dissents, and Justice KIRSHBAUM joins in the dissent.. We also granted certiorari on the question of whether the court of appeals erred in applying the doctrine of judicial estoppel. Because we conclude that the court of appeals did not err in applying the doctrine of collateral estoppel, we need not, and do not, consider whether the court of appeals erred in its application of judicial estoppel. See, e.g., Industrial Comm'n v. Moffat County School Dist. RE No. 1, 732 P.2d 616, 620 (Colo.1987).
. Bennett College’s one-quarter interest in the trust corpus is worth more than $7 million.
.After Bennett College filed for bankruptcy, Pace University, located in New York City, agreed inter alia to assume Bennett College’s student loan administration obligations, maintain the college’s records, raise funds for the Bennett Foundation, administer a Bennett College scholarship fund, and permit the college’s alumnae office to operate on the university’s property.
. Although Gage named Bennett School and Bennett Junior College, Bennett College's predecessors, as the trust beneficiaries, we refer to the school and junior college as "Bennett College.” The parties do not dispute that Bennett College is not in privity with Bennett School and Bennett Junior College.
. Under New York law, in certain charitable trust proceedings the attorney general is deemed to be the representative of the state of New York and charitable trust beneficiaries, and notice of such trust proceedings must be served on the attorney general. N.Y.Est. Powers & Trusts Law § 8 — 1.1(g)—(h) (McKinney 1967); 1971 N.Y. Laws 2641-42.
.The trust corpus in 1979 was worth $465,-983.37.
. The Bennett College bankruptcy proceedings, initiated in May 1977, were governed by the Bankruptcy Act. See Bankruptcy Reform Act of 1978, Pub.L. 95-598, § 403(a), 92 Stat. 2549, 2683 (1978).
. To the extent that they are relevant to this case, the cases cited by the Colleges are consistent with our recognition that the Bankruptcy Trustee was in privity with Bennett College, the debtor in bankruptcy, in the Gage trust court proceedings. For example, DePinto v. United States, 407 F.Supp. 5, 7 (D.Ariz.1976), aff’d, 585 F.2d 405 (9th Cir.1978), states that a bankruptcy trustee has a "duty to represent the creditors and to realize the maximum profit on the bankruptcy estate.”
.The trustee suspended trust payments to Bennett College on September 6, 1977, because of concerns about whether the college continued to exist, as the Gage trust deed required. Bennett College was adjudicated bankrupt on October 14, 1977.
. We note that, as the Colleges acknowledge, Bennett College was served with notice that the New York Supreme Court had issued an order to show cause directing Bennett College, and the other parties interested in the Gage trust, to appear before the court to show cause why the court should not make a determination of whether Bennett College had ceased to exist. However, no personal representative from the college appeared at the proceeding to show cause.