Recent claims by politicians and others PolitiFact checked out included President Trump's assertion of his administration's mightier effort than his predecessor against ISIS; Sen. Edward Markey's claim of an increase in HIV linked to heroin and fentanyl use; and Trump's calling the diversity visa lottery program "a Chuck Schumer beauty." Here are summaries of our findings. Full versions can be found at www.politifact.com.

“We have done more in eight months than the previous administration has done in many years” against ISIS.

— President Donald Trump on Wednesday, Oct. 25, 2017

Based on numbers from the battlefield and the assessment of terrorism analysts, Trump can rightly claim that he built on the work done under President Barack Obama, but he can’t take full ownership of the gains that followed.

The campaign to defeat ISIS took shape in September 2014, named Operation Inherent Resolve. Counting only sorties in which at least one weapon was released, about three-fourths of the action took place during the Obama years. The Air Force reports over 102,000 missiles, bombs and other explosives dropped in the campaign. Over two-thirds of that came before Trump took office.

By late August 2014, the Islamic State controlled about 35,000 square miles. Most of the territorial collapse took place during the Trump administration. But offensive operations began under Obama. Under Trump, airstrikes increased, and military commanders were given greater leeway to order attacks.

Our ruling

The Islamic State has suffered its largest territorial losses since Trump took office, but between two-thirds and three-fourths of the firepower unleashed against ISIS hit before Trump became president. While Trump ordered some changes in the military operation, the experts we reached said those didn’t transform the strategy so much as continue the one he inherited from Obama.

We rate this claim Half True.

Says HIV and AIDS rates have spiked “due to increased heroin and fentanyl use.”

— Sen. Edward Markey, D-Mass., on Thursday, Oct. 26, 2017 in a statement

We found some truth to Markey’s claim but not enough national data to fully back it.

The Centers for Disease Control and Prevention told us it does not have data specific to heroin and fentanyl, and it estimates that HIV and AIDs diagnoses have declined in recent years among people who inject drugs.

Experts we reached said they were not aware of reports showing a national spike in HIV and AIDS among injection drug users, but noted that data collection and reporting tends to lag.

Our ruling

There are risks for HIV transmission among people who share needles and syringes to inject opioids. An Indiana county recently had an HIV outbreak linked to the injection of opioids, including heroin. At least 220 U.S. counties may be at risk of similar outbreaks. But the CDC said it does not have national data addressing Markey’s heroin and fentanyl claim, and estimates that HIV and AIDs diagnoses have declined in recent years among people who inject drugs.

Markey's statement contains an element of truth but ignores critical facts that would give a different impression. We rate it Mostly False.

Says the diversity visa lottery program is “a Chuck Schumer beauty.”

— President Donald Trump on Wednesday, Nov. 1, 2017 in a tweet

Schumer was involved in the program's creation, but the bill passed by both houses included support by many Republicans, including Mitch McConnell, R-Ky., now Senate Majority Leader; John McCain of Arizona, and Dan Coats, Trump's director of national intelligence.

And, in 2013 Schumer was one of the bipartisan “gang of eight” that negotiated a bill that would have eliminated the diversity lottery. It passed the Senate 68-32 but died when members who support low levels of immigration, predominantly Republicans, prevented action in the GOP-controlled House.

Our ruling

Schumer did introduce legislation 27 years ago that eventually established the diversity visa lottery. The bill was signed by a Republican president, and the final version received majority Republican support in both chambers of Congress. Trump’s tweet ignores Schumer’s effort just four years ago to pass a bill that would have ended the lottery, which died due to Republican opposition in the House.

We rate the statement Mostly False.