I don't believe anyone has ever asked them to accept these definitions. Bl. Pius IX certainly did not. He wrote his encyclical to the east and sent it out at large rather than to the Bishops, who of course he did not invite to Vatican I, an act tantamount to a giant slap in the face. Bl. John XXIII didn't either. He couldn't even figure out how to invite the eastern Bishops to the Vatican to address the topic beyond two comprimised Russians.
As far as the jurisdiction of Rome, the east does recognize the right of appeal, which is the only matter of jurisdiction with any real bearing upon them (unless of course an ecumenical council sees fit to reorder the jurisdictions of the Church). It is enshrined in several councils in Constantinople between 861 and 880. The ordinary and immediate jurisdiction of the Pope means that he is able to deal as the final arbiter with all Christians, not that all jurisdictional actions are rightfully his own power, and only exercised by others (like say, another Bishop), because he happens to give them some power. Maybe its too obvious to say this - but the other Apostles derived their power from Christ, not from St. Peter. So also with all Bishops.
Most of what Latin rite Catholics think of as the jurisdiction of Rome is a matter of concern only to us in so far as the Pope is Patriarch of the West, and not as Pope. The Pope does not have the right, for example, to appoint Bishops to the eastern Churches in union with Rome, unlike the Church in the US.
Ask an Orthodox though. Do they agree that when the Bishop of Rome and the Eastern Bishops were in communion, that the Bishop of Rome was the court of final appeal? If communion were restored would he be so again? I think you'll find the answer is yes, simply because it is a well established historical fact mentioned a number of times in the Canons and Councils. What we term the infallibility of the Pope flows from his possession of this right of appeal. Obviously, an inerrant Church cannot have an errant final decision maker in doctrinal matters. This is the same reason that Ecumenical Councils are infallible.
All these accusations of heresy from both sides simply cloud the actual problem - the breach in communion between Rome and the Bishops of the East.
Furthermore, they profess that Christian marriage can be dissolved in total contradiction to the Council of Trent, a doctrine that Leo XIII called a "baneful heresy" (Arcanum Divinae §33).
The definition at Trent was written with an eye towards not condemning eastern practice (the note in Denzinger reads: "This form of condemnation was chosen lest the Greeks be offended, who evidently followed a contrary practice, although they did not condemn the opposite practice of the Latin Church."). What they term "ecclesiastical divorce" is little different than what we term "annulment". Why not ask an Easterner about it instead of shading the truth?
I'd think "So then, should anyone, which God forbid, have the temerity to reject this definition of ours: let him be anathema." would do. And of course infallibility is rejected in the Patriarchal Encyclical of 1895.
Bl. Pius IX certainly did not. He wrote his encyclical to the east and sent it out at large rather than to the Bishops, who of course he did not invite to Vatican I, an act tantamount to a giant slap in the face.
"Bishops from the eastern Orthodox Churches were also invited, but did not come." - this is from the "Introduction" to Vatican I on the EWTN website.
The ordinary and immediate jurisdiction of the Pope means that he is able to deal as the final arbiter with all Christians, not that all jurisdictional actions are rightfully his own power, and only exercised by others (like say, another Bishop), because he happens to give them some power. Maybe its too obvious to say this - but the other Apostles derived their power from Christ, not from St. Peter. So also with all Bishops.
That doesn't seem so obvious to me:
Yet in exercising this office they are not altogether independent, but are subordinate to the lawful authority of the Roman Pontiff, although enjoying the ordinary power of jurisdiction which they receive directly from the same Supreme Pontiff. (Pius XII, Encyclical Mystici Corporis Christi §42)
The definition at Trent was written with an eye towards not condemning eastern practice (the note in Denzinger reads: "This form of condemnation was chosen lest the Greeks be offended, who evidently followed a contrary practice, although they did not condemn the opposite practice of the Latin Church."). What they term "ecclesiastical divorce" is little different than what we term "annulment". Why not ask an Easterner about it instead of shading the truth?
This doesn't seem right to me:
If, however, a marriage breaks down and collapses, the Orthodox Church does in fact allow a second marriage, without excommunication, that is, exclusion from Holy Communion, if there is repentance and a good chance that the new alliance can be Christian. (OCA website)
Either the marriage has dissolved (it can't break down if it never existed), or there are in fact two marriages.
CANON II.-If any one saith, that it is lawful for Christians to have several wives at the same time, and that this is not prohibited by any divine law; let him be anathema.CANON VlI.-If any one saith, that the Church has erred, in that she hath taught, and doth teach, in accordance with the evangelical and apostolical doctrine, that the bond of matrimony cannot be dissolved on account of the adultery of one of the married parties; and that both, or even the innocent one who gave not occasion to the adultery, cannot contract another marriage, during the life-time of the other; and, that he is guilty of adultery, who, having put away the adulteress, shall take another wife, as also she, who, having put away the adulterer, shall take another husband; let him be anathema.
The third is the indissolubility of marriage, since it signifies the indivisible union of Christ and the church. Although separation of bed is lawful on account of fornication, it is not lawful to contract another marriage, since the bond of a legitimately contracted marriage is perpetual. (Florence, Decree for the Armenians)
33. It must consequently be acknowledged that the Church has deserved exceedingly well of all nations by her ever watchful care in guarding the sanctity and the indissolubility of marriage. Again, no small amount of gratitude is owing to her...for having in many ways condemned the habitual dissolution of marriage among the Greeks;5353 Council of Florence and instructions of Eugene IV to the Armenians Benedict XIV, constitution Etsi Pastoralis, May 6, 1742. (Leo XIII, Arcanum)
Leo XIII says that the Greek practice is condemned.