This book grew out of my interest in what is common to three disciplines: mathematics, philosophy, and history. The origins of Zermelo's Axiom of Choice, as well as the controversy that it engendered, certainly lie in that intersection. Since the time of Aristotle, mathematics has been concerned alternately with its assumptions and with the objects, such as number and space, about which those assumptions were made. In the historical context of Zermelo's Axiom, I have explored both the vagaries and the fertility of this alternating concern. Though Zermelo's research has provided the focus for this book, much of it is devoted to the problems from which his work originated and to the later developments which, directly or indirectly, he inspired. A few remarks about format are in order. In this book a publication is indicated by a date after a name; so Hilbert 1926, 178 refers to page 178 of an article written by Hilbert, published in 1926, and listed in the bibliography.

THE INSTANT NEW YORK TIMES BESTSELLER The alternate history first contact adventure Axiom's End is an extraordinary debut from Hugo finalist and video essayist Lindsay Ellis. Truth is a human right. It’s fall 2007. A well-timed leak has revealed that the US government might have engaged in first contact. Cora Sabino is doing everything she can to avoid the whole mess, since the force driving the controversy is her whistleblower father. Even though Cora hasn’t spoken to him in years, his celebrity has caught the attention of the press, the Internet, the paparazzi, and the government—and with him in hiding, that attention is on her. She neither knows nor cares whether her father’s leaks are a hoax, and wants nothing to do with him—until she learns just how deeply entrenched her family is in the cover-up, and that an extraterrestrial presence has been on Earth for decades. Realizing the extent to which both she and the public have been lied to, she sets out to gather as much information as she can, and finds that the best way for her to uncover the truth is not as a whistleblower, but as an intermediary. The alien presence has been completely uncommunicative until she convinces one of them that she can act as their interpreter, becoming the first and only human vessel of communication. Their otherworldly connection will change everything she thought she knew about being human—and could unleash a force more sinister than she ever imagined.

The crew of the White Raven returns to save the galaxy, in this brilliant space opera sequel to The Wrong Stars Ancient aliens, the Axiom, will kill us all – when they wake up. In deep space, a swarm of nanoparticles threatens the colonies, transforming everything it meets into computronium – including the colonists. The crew of the White Raven investigate, and discover an Axiom facility filled with aliens hibernating while their minds roam a vast virtual reality. Sebastien wakes up, claiming his altered brain architecture can help the crew deactivate the swarm – from inside the Axiom simulation. To protect humanity, Callie must trust him, but if Sebastien still plans to dominate the universe using Axiom tech, they could be in a whole lot of trouble… File Under: Science Fiction [ Nanowar | Let Sleeping Gods Lie | Upgraded | For the Colony ]

Philip K. Dick Award Finalist: A ragtag space crew discovers alien technology that could change the fate of humanity—or awaken an ancient evil that could destroy all life in the galaxy The shady crew of the White Raven run freight and salvage at the fringes of our solar system. They discover the wreck of a centuries-old exploration vessel floating light years away from its intended destination and revive its sole occupant, who wakes with news of First Alien Contact. When the crew informs her that humanity has alien allies already, she reveals that these are very different extra-terrestrials—and the gifts they bestowed on her could kill all humanity, or take it out to the most distant stars. “Ridiculously fun with a well-thought-out space opera setting and lots of fancy reveals.” —Charlie Jane Anders, author of All the Birds in the Sky “Through his wit, dialogue, and vast, diverse world, Tim Pratt has created a space opera for today—one filled with diverse characters and cultures that feel nuanced enough to be real—while still delivering the sense of wonder that made you love the genre in the first place.” —Barnes & Noble Sci-Fi & Fantasy Blog

Offers advice on investment strategy and risk management, clears up common misconceptions about the stock market, and discusses economic forecasts and long-range planning.

This “witty, heartfelt sci-fi romp” is the dazzling third installment in a diverse space opera series for fans of The Expanse and John Scalzi’s The Collapsing Empire—from a Hugo Award–winning author (Tor.com) The ancient alien gods are waking up—and there’s only one spaceship crew ready to stop them . . . Aliens known as the Liars gave humanity access to the stars through twenty-nine wormholes. They didn’t mention that other aliens, the ancient, tyrannical—but thankfully sleeping—Axiom occupied all the other systems. When the twenty-ninth fell silent, humanity chalked it up to radical separatists and moved on. But now, on board the White Raven, Captain Callie and her crew of Axiom-hunters receive word that the twenty-ninth colony may have met a very different fate. With their bridge generator, they skip past the wormhole—and discover another Axiom project, fully awake, and poised to pour through the wormhole gate into all the worlds of humanity . . .

Comprehensive and self-contained text examines the axiom's relative strengths and consequences, including its consistency and independence, relation to permutation models, and examples and counterexamples of its use. 1973 edition.