By and large, media coverage of the Trump-Putin summit in Helsinki has focused on the two leaders’ comments regarding Russian meddling in the 2016 presidential election, with Putin denying any involvement whatsoever and Trump swearing he believes the Russian president just as much as (if not more than) his own intelligence agencies—a stance that has triggered a tsunami of outrage from Democrats (and more than a few Republicans) back home. But however justified the outrage, concentrating solely on those exchanges would mean missing the principal outcome of the summit: Trump’s and Putin’s rollout of what could become a new model of international relations based on their joint, monopolistic management of world affairs.

From what can be gleaned from their public comments, the two mainly discussed how to transform the troubled US-Russian relationship from one of hostility and friction to one of accommodation and collaboration. Although acknowledging key differences on many issues, such as Crimea and the Iran nuclear deal, both said they will aim to find common ground wherever possible and to cooperate in preventing regional disputes from undermining their core interests.

Both presidents came back to this point repeatedly, suggesting that they might have decided in their private discussion to make this the main culmination of the summit.

“As major nuclear powers, we bear special responsibility for maintaining international security,” Putin began. This entailed, he indicated, cooperating in nuclear nonproliferation and counterterrorism. “We also mentioned a plethora of regional crises. It’s not always that our postures dovetail exactly, and yet the overlapping and mutual interests abound. We have to look for points of contact and interact closer in a variety of international forums.”

Syria, he explained, is an area that provides a model for such coordination. “Both Russian and American military have acquired the useful experience of coordination of their action, established the operational channels of communication which permit it to avoid dangerous incidents and unintentional collisions in the air and in the ground.”

Trump used much the same language to describe his new working relationship with the Russian leader.

“The disagreements between our two countries are well known and President Putin and I discussed them at length today,” he declared. “But if we’re going to solve many of the problems facing our world, then we’re going to have to find ways to cooperate in pursuit of shared interests.”

Like Putin, Trump spoke of the need for further cooperation in nuclear nonproliferation and counterterrorism. “Both Russia and the United States have suffered horrific terrorist attacks, and we have agreed to maintain open communication between our security agencies to protect our citizens from this global menace,” he noted.

But he went further than this, endorsing Putin’s suggestion for military coordination in contested areas like Syria. “Cooperation between our two countries has the potential to save hundreds of thousands of lives [in Syria],” Trump asserted, without explaining how. Then, in an extraordinary move, he proposed future coordination between top US and Russian security officials in overcoming upheavals of this sort. “We also agreed that representatives from our national-security councils will meet to follow up on all of the issues we addressed today”—an almost inconceivable step for two countries whose armed forces are poised for war with each other in various parts of the world.

There’s more of this in the transcript of their press conference, all channeling the same concept: that despite our differences, the top leaders of the United States and Russia are best positioned to consider any disturbances arising on the peripheries of their respective spheres of influence and at devising outcomes to the mutual benefit of both—irrespective of the welfare or preferences of any peoples caught up in these upheavals.

At one point, Trump expressed sympathy for the victims of the carnage in Syria. “You have such horrible—if you see—and I’ve seen reports, I’ve seen pictures, I’ve seen just about everything.” But it never crossed his mind that those people should have any voice in the outcome of the fighting there; that is something for the likes of Trump and Putin, and their military subordinates, to solve. Not to mention that both the Russian and US militaries have relied on airpower to achieve their strategic aims—Russia to defeat the anti-Assad rebels, the United States to crush ISIS—causing vast numbers of civilian casualties in each case.

As far as Syria goes, Trump noted, “our militaries do get along very well.” Putin added his assent to this: “I agree, I concur with President Trump, our military cooperate quite successfully together. They do get along and I hope they will be able to do so in future.”

In sum, the message coming from all this is that existing international institutions—the UN, NATO, the European Union—have lost their effectiveness as instruments of problem-solving and conflict resolution, and that only Russia and the United States, by virtue of their superior military power and (in their eyes) supremely talented leaders, are able to resolve major regional disputes. Because both great powers have an interest in preserving global stability, problems can be solved through periodic consultations between their leaders, like the meeting in Helsinki.

We will be hearing a lot about Trump’s and Putin’s comments about Russia’s involvement in the 2016 election over the coming days, but we should not ignore the implications of the Trump-Putin embrace of this new approach to global management and its centralization of world power in the hands of two nuclear-armed megalomaniacs. The erosion of democracy at home is of great concern, to be sure, but so is its disappearance on the world stage.