This is an expository account of work on strong forms of the Axiom of Determinacy (AD) by a group of set theorists in Southern California, in particular by W. Hugh Woodin. The first half of the book reviews necessary background material, including the Moschovakis Coding Lemma, the existence of strong partition cardinals, and the analysis of pointclasses in models of determinacy. The second half of the book introduces Woodin's axiom system $\mathrm{AD}^{+}$ and presents his initial analysis of these axioms. These results include the consistency of $\mathrm{AD}^{+}$ from the consistency of AD, and its local character and initial motivation. Proofs are given of fundamental results by Woodin, Martin, and Becker on the relationships among AD, $\mathrm{AD}^{+}$, the Axiom of Real Determinacy, and the Suslin property. Many of these results are proved in print here for the first time. The book briefly discusses later work and fundamental questions which remain open. The study of models of $\mathrm{AD}^{+}$ is an active area of contemporary research in set theory. The presentation is aimed at readers with a background in basic set theory, including forcing and ultrapowers. Some familiarity with classical results on regularity properties for sets of reals under AD is also expected.
This is an expository account of work on strong forms of the Axiom of Determinacy (AD) by a group of set theorists in Southern California, in particular by W. Hugh Woodin. The first half of the book reviews necessary background material, including the Moschovakis Coding Lemma, the existence of strong partition cardinals, and the analysis of pointclasses in models of determinacy. The second half of the book introduces Woodin's axiom system $\mathrm{AD}^{+}$ and presents his initial analysis of these axioms. These results include the consistency of $\mathrm{AD}^{+}$ from the consistency of AD, and its local character and initial motivation. Proofs are given of fundamental results by Woodin, Martin, and Becker on the relationships among AD, $\mathrm{AD}^{+}$, the Axiom of Real Determinacy, and the Suslin property. Many of these results are proved in print here for the first time. The book briefly discusses later work and fundamental questions which remain open. The study of models of $\mathrm{AD}^{+}$ is an active area of contemporary research in set theory. The presentation is aimed at readers with a background in basic set theory, including forcing and ultrapowers. Some familiarity with classical results on regularity properties for sets of reals under AD is also expected.
Metaphysics has often held that laws of nature, if legitimate, must be time-independent. Yet mounting evidence from the foundations of science suggests that this constraint may be obsolete. This book...
In this volume the author develops and applies methods for proving, from large cardinals, the determinacy of definable games of countable length on natural numbers. The determinacy is ultimately...
Law, Language, and Legal Determinancy discusses the role of language within law, and the role of philosophy of language in understanding the nature of law. The book argues that the major re-thinking...
This book investigates the phenomenon of semantic under-determinacy by arguing for its distinctiveness and non-reducibility to other familiar phenomena, and addresses the question of how...
Discover your next great read at BookLoop, Australiand online bookstore offering a vast selection of titles across various genres and interests. Whether you're curious about what's trending or searching for graphic novels that captivate, thrilling crime and mystery fiction, or exhilarating action and adventure stories, our curated collections have something for every reader. Delve into imaginative fantasy worlds or explore the realms of science fiction that challenge the boundaries of reality. Fans of contemporary narratives will find compelling stories in our contemporary fiction section. Embark on epic journeys with our fantasy and science fiction titles,
Shop Trending Books and New Releases
Explore our new releases for the most recent additions in romance books, fantasy books, graphic novels, crime and mystery books, science fiction books as well as biographies, cookbooks, self help books, tarot cards, fortunetelling and much more. With titles covering current trends, booktok and bookstagram recommendations, and emerging authors, BookLoop remains your go-to local australian bookstore for buying books online across all book genres.
Shop Best Books By Collection
Stay updated with the literary world by browsing our trending books, featuring the latest bestsellers and critically acclaimed works. Explore titles from popular brands like Minecraft, Pokemon, Star Wars, Bluey, Lonely Planet, ABIA award winners, Peppa Pig, and our specialised collection of ADHD books. At BookLoop, we are committed to providing a diverse and enriching reading experience for all.
Sign In
your cart
Your cart is empty
Menu
Search
PRE-SALES
If you have any questions before making a purchase chat with our online operators to get more information.
