New York (CNN) President Donald Trump on Tuesday seized on the nationalist ideology that fueled his political rise -- and took it to the United Nations .

The President's speech to the UN General Assembly made clear to the world and to the American public that the President is sticking firmly to his "America First" vision of US foreign policy and abiding by much of the rhetoric he has used to articulate that vision -- both on the campaign trail and since taking office.

Here are some phrases that defined Trump's speech:

'Sovereign' or 'sovereignty'

Trump deployed these terms 21 times as he made the case that strong, independent nations -- rather than international institutions -- are the key to unlocking a more prosperous and peaceful future.

The word "sovereign" is the embodiment of Trump's "America First" vision of US foreign policy, and Trump made clear to the world that the US will ultimately act in its own self-interest and said that other countries would naturally do the same.

"In foreign affairs, we are renewing this founding principle of sovereignty. Our government's first duty is to its people, to our citizens, to serve their needs, to ensure their safety, to preserve their rights and to defend their values," Trump said. "I will always put America first, just like you, as the leaders of your countries, will always and should always put your countries first."

Trump also said that sovereignty can be a "call for action," noting that "all people deserve a government that cares for their safety, their interests and their well-being."

But it was the President's repeated emphasis on these terms that sent an unambiguous message to world leaders -- particularly those hopeful that Trump might soften his nationalist ideology in favor of a more cooperative bend toward the world -- that he is still strongly committed to the nationalist principles that fueled his political rise.

'Radical Islamic terrorism'

In vowing Tuesday that "we will stop radical Islamic terrorism," Trump dimmed hopes that he had begun to understand the damaging impact the controversial phrase can have on relations with Muslims in the US and abroad.

Many of the President's foreign policy advisers -- most notably national security adviser Lt. Gen. H.R. McMaster -- have urged him to drop his use of the phrase, which associates terrorism with the religion of Islam.

Trump's prepared remarks for his speech in Saudi Arabia called for him to say "Islamist extremism" instead -- a phrase used to distinguish between the religion of more than a billion people around the world and the fundamentalist political ideology that drives terrorist groups like ISIS and al Qaeda.

Even during that speech, Trump used the phrase "Islamic extremism," which a senior White House official later attributed to the President's fatigue from the international travel.

"Just an exhausted guy," the official had said.

But Trump's use of the phrase Tuesday was a signal to his base that the President is still behind his hardline views on terrorism -- particularly after a week during which he's wavered on other campaign promises that animated his base, like protections for certain undocumented immigrants.

'Rocket Man'

After first tweeting it days earlier, Trump himself publicly uttered his new moniker for the North Korean dictator during his speech on Tuesday.

A senior administration official told CNN's Jim Acosta the "Rocket Man" term was a late addition to the President's formal speech -- added this morning.

The nickname, coupled with his vow to "totally destroy North Korea" if need be, made clear that Trump still firmly believes in the power of dramatic rhetoric as a tool in his ongoing confrontation with North Korea's leader, Kim Jong Un.

Trump's rhetoric regarding North Korea on Tuesday was reminiscent of his over-the-top vow to rain "fire and fury" on North Korea if its provocations continue.

Trump's warning that the US would "totally destroy" North Korea to defend itself or its allies left many diplomats and UN officials stunned in the foremost forum for international diplomacy.

"You could feel a wind had gone into the room when he said that. People were taken aback," a senior UN diplomat told CNN.

Words not said about Russia and China

Beyond the specific terms he did use to drive home his message on Tuesday, the absence of other words also served to define the President's dispatch to the world.

While Trump offered unencumbered criticism of countries like North Korea, Cuba and Venezuela, he delivered no direct condemnation of China and Russia -- countries whose policies have had a destabilizing impact on the US on the world stage.

Instead, there were only vague references to "threats to sovereignty, from the Ukraine to the South China Sea." He also called out countries that trade with North Korea, labeling the practice "an outrage."

But while China is responsible for the overwhelming majority of trade with North Korea, Trump's lack of direct criticism of the two countries gave insight into the President's approach to the US' disagreements and often adversarial relationships with the two countries -- particularly at a time when he needs the two countries to support US efforts to ramp up pressure on North Korea.

Instead of direct criticism, Trump instead offered praise for China and Russia, thanking them by name "for joining the vote to impose sanctions" on North Korea.

'Culture'

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Embedded in Trump's speech was a deeper layer to the nationalist stance he firmly relayed.

As he emphasized the importance of the "nation-state" -- a country defined by a singular national identity -- Trump also expressed elements of his hardline views on immigration and stressed the importance of respecting -- and maintaining -- the distinctive cultures of various countries.

"We must uphold respect for law, respect for borders and respect for culture, and the peaceful engagement these allow," Trump said.

Later, he asked whether countries "revere" their own citizens enough "to defend their interests, preserve their cultures and ensure a peaceful world for their citizens?"

Trump -- who has sought to limit both legal and illegal immigration into the US, called for building a wall on the US-Mexico border and limited the admission of refugees into the US -- addressed immigration more explicitly as well.

He referred to the costs of "long-term uncontrolled migration" and promoted keeping refugees in or near their home countries -- rather than resettling them in far-flung countries like the United States.