Boolean-valued models and independence proofs in set theory (Oxford logic guides)

Science & Math

Bell, J.L.

Mathematics

Oxford University Press

The author introduces Lawvere and Tierney's concept of topos theory, a striking development in category theory that unites a number of important but seemingly diverse notions from algebraic geometry, set theory, and intuitionistic logic. Topos theory has led to the forging of surprising new links between classical and constructive mathematics. Bell presents toposes as the models of theories--the so-called local set theories--formulated within a typed intuitionistic logic.

Toposes and Local Set Theories: An Introduction (Oxford Logic Guides)

Includes experiments involving various kinds of soap and soap bubbles to demonstrate how soap works and to help explore electricity, light, and other science topics

Soap Science: A Science Book Bubbling With 36 Experiments

Children's Books

Literature & Fiction

Addison-Wesley

In this text for first-year graduate students, the authors provide an elementary exposition of some of the basic concepts of model theory--focusing particularly on the ultraproduct construction and the areas in which it is most useful. The book, which assumes only that its readers are acquainted with the rudiments of set theory, starts by developing the notions of Boolean algebra, propositional calculus, and predicate calculus. Model theory proper begins in the fourth chapter, followed by an introduction to ultraproduct construction, which includes a detailed look at its theoretic properties. An overview of elementary equivalence provides algebraic descriptions of the elementary classes. Discussions of completeness follow, along with surveys of the work of Jónsson and of Morley and Vaught on homogeneous universal models, and the results of Keisler in connection with the notion of a saturated structure. Additional topics include classical results of Gödel and Skolem, and extensions of classical first-order logic in terms of generalized quantifiers and infinitary languages. Numerous exercises appear throughout the text.

Models and Ultraproducts: An Introduction (Dover Books on Mathematics)

Slomson, A. B.

Biological Sciences

Dover Publications

Topos theory has led to unexpected connections between classical and constructive mathematics. This text explores Lawvere and Tierney's concept of topos theory, a development in category theory that unites important but seemingly diverse notions from algebraic geometry, set theory, and intuitionistic logic. A virtually self-contained introduction, this volume presents toposes as the models of theories — known as local set theories — formulated within a typed intuitionistic logic. The introductory chapter explores elements of category theory, including limits and colimits, functors, adjunctions, Cartesian closed categories, and Galois connections. Succeeding chapters examine the concept of topos, local set theories, fundamental properties of toposes, sheaves, locale-valued sets, and natural and real numbers in local set theories. An epilogue surveys the wider significance of topos theory, and the text concludes with helpful supplements, including an appendix, historical and bibliographical notes, references, and indexes.

Toposes and Local Set Theories: An Introduction (Dover Books on Mathematics)

In this text for first-year graduate students, the authors provide an elementary exposition of some of the basic concepts of model theory--focusing particularly on the ultraproduct construction and the areas in which it is most useful. The book, which assumes only that its readers are acquainted with the rudiments of set theory, starts by developing the notions of Boolean algebra, propositional calculus, and predicate calculus.Model theory proper begins in the fourth chapter, followed by an introduction to ultraproduct construction, which includes a detailed look at its theoretic properties. An overview of elementary equivalence provides algebraic descriptions of the elementary classes. Discussions of completeness follow, along with surveys of the work of Jónsson and of Morley and Vaught on homogeneous universal models, and the results of Keisler in connection with the notion of a saturated structure. Additional topics include classical results of Gödel and Skolem, and extensions of classical first-order logic in terms of generalized quantifiers and infinitary languages. Numerous exercises appear throughout the text.

Models and ultraproducts

North-Holland Publishing Company

Product Description A comprehensive one-year graduate (or advanced undergraduate) course in mathematical logic and foundations of mathematics. No previous knowledge of logic is required; the book is suitable for self-study. Many exercises (with hints) are included. Review The book is valuable for anyone interested in mathematical logic and may serve as a reference source for graduate students and specialists.Zentralblatt für Mathematik

A Course in Mathematical Logic

Computers & Technology

Machover, M.

Computer Science

North-Holland

With a Clash Between American Rebels and Royal Authorities Heating Up, Radicals Smuggled Cannon Out of Boston—and the British Came Looking for Them In the early spring of 1775, on a farm in Concord, Massachusetts, British army spies located four brass cannon belonging to Boston’s colonial militia that had gone missing months before. British general Thomas Gage had been searching for them, both to stymie New England’s growing rebellion and to erase the embarrassment of having let cannon disappear from armories under redcoat guard. Anxious to regain those weapons, he drew up plans for his troops to march nineteen miles into unfriendly territory. The Massachusetts Patriots, meanwhile, prepared to thwart the general’s mission. There was one goal Gage and his enemies shared: for different reasons, they all wanted to keep the stolen cannon as secret as possible. Both sides succeeded well enough that the full story has never appeared until now. The Road to Concord: How Four Stolen Cannon Ignited the Revolutionary War by historian J. L. Bell reveals a new dimension to the start of America’s War for Independence by tracing the spark of its first battle back to little-known events beginning in September 1774. The author relates how radical Patriots secured those four cannon and smuggled them out of Boston, and how Gage sent out spies and search parties to track them down. Drawing on archives in the United States, United Kingdom, and Canada, the book creates a lively, original, and deeply documented picture of a society perched on the brink of war.

The Road to Concord: How Four Stolen Cannon Ignited the Revolutionary War (Journal of the American Revolution Books)

History

Americas

Westholme Publishing

Welcome to a universe of wonder! What's it like to have a mad scientist for a father? Or protect your sleeping city from the terrors of the deep, or save your family spaceship? Blast off for new worlds with the Young Explorer's Adventure Guide Volume 6! "This stellar collection will appeal to both teens and grown-ups who dream of future worlds." Kirkus Review of Books, for the 2018 Young Explorer's Explorer's Guide

Young Explorer's Adventure Guide, Volume 6

Kress, Nancy

Bell, Dana

Del Carlo, Eric

Angway, Marilag

Black, A. Katherine

Bushmore, John

Davis, L.H.

Forier Edie, Elise

gibson, anne m.

Dreaming Robot Press

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Books by Bell, J.L.