WASHINGTON (AP) — The vast complexities of a dangerous world were cast in too-simple terms in the latest Republican presidential debate.
In addition, Chris Christie pledged to make common cause with a Jordanian king who's actually dead and debaters twisted aspects of immigration policy beyond recognition.
Here's a look at some of the claims Tuesday night and how they compare with the facts:
TED CRUZ on immigration policy: "What you do is you enforce the law... That means you stop the Obama administration's policy of releasing criminal illegal aliens. Do you know how many aliens Bill Clinton deported? 12 million. Do you know how many illegal aliens, George W. Bush deported? 10 million."
THE FACTS: Cruz vastly overstates the deportation numbers for both presidents. Statistics from Immigration and Customs Enforcement show that roughly 1.6 million were deported under Bush. Under Clinton, when the old Immigration and Naturalization Service oversaw deportations, the figure was about 870,000, according to the Migration Policy Institute. So far, about 2.4 million have been deported under the Obama administration.
To get the larger numbers, Cruz appears to be combining deportations with arrests made by the Border Patrol in the previous administrations, the institute says.
CRUZ on people in the U.S. illegally: "I have never supported legalization, and I do not intend to support legalization."
THE FACTS: That flies in the face of the Texas senator's record and past rhetoric. Cruz has indeed been against an explicit path to citizenship for people in the country illegally, but he introduced legislation in 2013 that proposed eventual legal status for millions of them.
His legislation proposed stripping out the option of citizenship from a bill overhauling immigration policy. Instead, he told the Senate in June 2013, his bill would set up a process so that "those who are here illegally would be eligible for what is called RPI (Registered Provisional Immigrant) status, a legal status, and, indeed, in time would be eligible for legal permanent residency."
Cruz defended that course on multiple occasions in the Senate and in interviews — usually stressing his objection to extending citizenship but also making clear he envisioned eventual work permits and other means of legal recognition short of citizenship.
The overarching effort to overhaul immigration policy that year failed. One of the principal authors of the initiative was Florida Sen. Marco Rubio, another presidential contender, and Cruz's claims emerged in a tussle between the two on the subject.
Also notable from Cruz's statement in the debate was that he subtly avoided closing the door to supporting legal status in the future. He said "I don't intend" to do that, which doesn't mean he won't.
DONALD TRUMP: "Our country is out of control. People are pouring through the southern border."
THE FACTS: Arrest statistics are widely regarded as the best measure, if an imperfect one, of the flow of people crossing illegally into the U.S. And Trump's suggestion that illegal immigration is increasing at the border is not supported by arrest statistics discussed in recent months by Homeland Security Secretary Jeh Johnson.
Johnson has said that during the 2015 budget year that ended in September, about 330,000 people were caught crossing the Mexican border illegally, a near 40-year low in border arrests. During the 2014 budget year, roughly 486,000 people were arrested.
In recent months there has been a spike in the arrests at the border, but primarily of children traveling alone and families, mostly from Central America.
CRUZ: "You would carpet bomb where ISIS is, not a city."
THE FACTS: The Texas senator's conviction that the Islamic State group can be routed with an air campaign of overwhelming force is hard to square with the reality on the ground. IS fighters are holed up in a variety of cities, amid civilians, raising questions about how he could direct a carpet bombing that only singles out the enemy.
He was asked in the debate if he'd be willing to cause civilian casualties in Raqqa, a major Syrian city that has become de facto capital of the Islamic State group's so-called caliphate. ISIS is also in control of the Iraqi city of Mosul.
JEB BUSH: "We need to embed our forces, our troops, inside the Iraqi military."
THE FACTS: The U.S. is already doing that.
U.S. special forces are working side by side with Iraqi forces in the fight against Islamic State militants and American military advisers and trainers are working with Iraqi troops in various locations. To be sure, Bush has called for an intensification of the military effort in a variety of ways, but debate viewers would not know from his comment that U.S. troops are already operating with Iraqi and Kurdish forces.
His comment fits a pattern in the Republican race as a number of candidates criticize President Barack Obama's course against IS while proposing largely the same steps that are already underway.
RAND PAUL: "Every terrorist attack we've had since 9/11 has been legal immigration."
THE FACTS: Not so.
One of the San Bernardino, California, attackers was 28-year-old Syed Farook, who was born in Illinois. Nidal Hasan, who perpetrated the 2009 Fort Hood shootings that killed 13 people, was not only an American but an Army major.
CHRISTIE: "When I stand across from King Hussein of Jordan and I say to him, 'You have a friend again sir, who will stand with you to fight this fight,' he'll change his mind."
THE FACTS: He won't, because he died in 1999. Jordan's king now is Abdullah II.
CRUZ: "And even worse, President Obama and Hillary Clinton are proposing bringing tens of thousands of Syrian refugees to this country when the head of the FBI has told Congress they cannot vet those refugees."
THE FACTS: Cruz repeated inflated estimates of how many Syrian refugees the Obama administration plans to admit to the United States. Obama has announced plans to resettle about 10,000 refugees in the next year.
The vetting process for refugees takes, on average, about two years and is routinely longer for refugees from Syria and Iraq. The administration has said refugees being considered for resettlement in the United States are subject to additional scrutiny. The administration has declined to describe what the scrutiny involves, saying it is classified.
TRUMP, responding to questions about his stated desire to "close" the Internet to terrorists: "This is so easy to answer. ISIS is recruiting through the Internet. ISIS is using the Internet better than we are using the Internet, and it was our idea. What I wanted to do is I wanted to get our brilliant people from Silicon Valley and other places and figure out a way that ISIS cannot do what they're doing."
THE FACTS: The Internet is so decentralized that no government can shut down parts of it, short of physically destroying major infrastructure. Websites aren't restricted by geography, can be located anywhere in the world and can move anywhere on short notice.
China, Iran and a few other nations have erected "firewalls" to prevent their citizens from connecting to particular websites but even those are leaky. No such firewall exists in the U.S. and would raise big free-speech issues if anyone attempted to build one.
MARCO RUBIO on facing terrorist threats: "We need more tools, not less tools. And that tool we lost, the metadata program, was a valuable tool that we no longer have at our disposal."
CRUZ: The USA Freedom Act passed by Congress ended the federal government's bulk collection of telephone metadata for all Americans, and "strengthened the tools of national security and law enforcement to go after terrorists."
THE FACTS: Both are right, but are emphasizing different aspects of the new law. While the government has lost speed and ability to reach back in time, it has gained volume of coverage.
The controversial NSA surveillance program revealed by leaker Edward Snowden had allowed the intelligence community to quickly analyze five years of calling records in search of connections among Americans and foreign terror suspects.
Under the new law, the government can no longer collect and store calling data. Instead, it has to request a search of data held by the phone companies, which typically hold the records for two years. It's unclear how quickly those searches can take place, but it's probably longer than in the previous system. Rubio is correct in this regard.
Cruz is correct that under the prior program, a large segment of mobile phone records went uncollected. Under the new regime, a larger universe of phone records can be searched.
What neither acknowledged is that the phone records program was not regarded inside NSA as an important tool in ferreting out terrorism plots. The only case the government has said was cracked because of the program over a decade was a relatively minor terrorist financing scheme.
Associated Press writers Alicia A. Caldwell, Ken Dilanian and David Hamilton contributed to this report.