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• Sales Rank: #3564440 in Books
• Published on: 2005
• Binding: Hardcover

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• Sales Rank: #4837618 in Books
• Published on: 2015-12-10
• Original language: English
• Number of items: 1
• Dimensions: 9.02" h x .39" w x 5.98" l, .57 pounds
• Binding: Paperback
• 170 pages

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[G604.Ebook] Free Ebook Cantorian Set Theory and Limitation of Size (Oxford Logic Guides), by Michael Hallett

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Cantor's ideas formed the basis for set theory and also for the mathematical treatment of the concept of infinity. The philosophical and heuristic framework he developed had a lasting effect on modern mathematics, and is the recurrent theme of this volume. Hallett explores Cantor's ideas and, in particular, their ramifications for Zermelo-Frankel set theory.

• Sales Rank: #3194553 in Books
• Published on: 1986-12-18
• Original language: English
• Number of items: 1
• Dimensions: 6.13" h x .82" w x 9.25" l, 1.21 pounds
• Binding: Paperback
• 343 pages

Review

"Here is the first full-length study to do justice both to the mathematical importance of Cantor's work and to the philosophical ideas that governed it....The book is very well informed mathematically, yet much of Hallett's perceptive comment on and his patient and sympathetic interpretation of the philosophical ideas of Cantor and the other founders of set theory will be readily intelligible to nonspecialists, making the book of great interest to mathematician and philosopher alike."--Choice

"Establishes a new plateau for historical comprehension of Cantor's monumental contribution to mathematics."--The American Mathematical Monthly

About the Author
Michael Hallett is at McGill University, Montreal.

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1 of 1 people found the following review helpful.
Cantorian Set Theory and Limitation of Size
By Sam Adams
Georg Cantor lived from 1845 to 1918. Judging from Hallet's bibliography, Cantor's publications on sets and infinity occurred in the years 1872 to 1897. A letter of 1899 to Richard Dedekind [1831-1916] is also relevant. This letter is the only writing by Cantor included in Jean van Heijenoort's From Frege to G�del: A Source Book in Mathematical Logic, 1879-1931. No letter or publication by Cantor later than 1899 is discussed in Hallet's book, although a letter from 1903 to Philip Jourdain [1879-1919] is mentioned as outlining the proof given in the 1899 letter to Dedekind, and a partial sentence is quoted from a letter to Jourdain in 1904. Ernst Zermelo [1871-1953] edited Cantor's collected works in 1932, published as Gesammelte Abhandlungen mathematischen und philosophischen Inhalts. Cantor's Contributions to the Founding of the Theory of Transfinite Numbers (translated in 1915 by Jourdain) date from 1895 and 1897, and are Cantor's last public presentations of his ideas.

Hallet's book does not contain biographical details on Cantor, and it is not a general history of the rise of set theory. It is foremost an account of Cantor's conception of infinity, both metaphysical and mathematical, and of Cantor's varied presentations, in publications and letters, of his theories of cardinal and ordinal numbers. Hallett focuses tightly on Cantor's writings as he meticulously traces the development of Cantor's ideas, and only after he has established Cantor's views does Hallett include the work of others, unless he gives a joint comparison with the focus on Cantor.

Cantor's set theory is not axiomatic, and although Hallett discusses to some degree, mainly in Part 2, the relationship of the axiomatic theory of sets to Cantor's conception of sets and infinity, the emphasis of the book is on Cantor's work, and only secondarily on the contributions of others as they explored and expanded on Cantor's ideas.

In the first two chapters of Part 2, Hallett is less concerned with how proposed axioms combine to define a theory of sets than with how certain axioms have been discussed and justified (for example, as a means of limiting the comprehension of sets or of representing the iterative conception of sets) and with the claim that the set theoretic paradoxes are meaningfully related to Kant's antinomies of pure reason.

In the final two chapters, Hallett discusses the differing systems of Zermelo and John von Neumann [1903-1957], where his focus in chapter seven is on Zermelo's axiom system in relation to his 1904 and 1908 proofs of the well-ordering theorem, and in chapter eight on von Neumann's theory of ordinals from 1923 (also anticipations of it by others), his use and clarification of the axiom of replacement first proposed by Abraham Fraenkel [1891-1965], and von Neumann's axiomatic theory of functions (not sets) of 1925.

= CONTENTS =
Preface [precedes Contents page]
* Part 1. The Cantorian origins of set theory
Introduction to Part 1: The background to the theory of the ordinals
1. Cantor's theory of infinity
__ 1.1 Free mathematics
__ 1.2 The potential infinite and reductionism
__ 1.3 Cantorian finitism and the concept of set
__ 1.4 Cantor's absolute
2. The ordinal theory of powers
__ 2.1 The generating principles
__ 2.2 The scale of number-classes
__ 2.3 The attack on the continuum problem
___ (a) First step: the uncountability of the continuum and the second number-class
___ (b) What did Cantor achieve?
___ (c) The continuum hypothesis and later developments
3. Cantor's theory of number
__ 3.1 Cantor's abstractionism, set reduction, and Frege-Russell
__ 3.2 Difficulties with the strange theory of 'ones'
__ 3.3 The theory of 'ones' sensibly constructed
__ 3.4 Order-types
__ 3.5 Cantor and well ordering
4. The origin of the limitation of size idea
__ 4.1 The Absolute and limitation of size
__ 4.2 Jourdain's limitation of size theory
__ 4.3 Modifying comprehension by limitation of size
__ 4.4 Mirimanoff
* Part 2. The limitation of size argument and axiomatic set theory
Introduction to Part 2
5. The limitation of size argument
__ 5.1 Fraenkel's argument criticized
__ 5.2 The explanatory role of limitation of size
__ 5.3 The power-set axiom
6. The completability of sets
__ 6.1 The iterative conception
__ 6.2 Completability and Kant's first antinomy
___ (a) Contradiction or sleight of hand?
___ (b) Completability and contructivity
7. The Zermelo system
__ 7.1 Zermelo's separation axiom as a limitation of size principle
__ 7.2 Zermelo's reductionism
___ (a) Zermelo's reductionist treatment of number
___ (b) Zermelo's reductionist treatment of contradiction
__ 7.3 Reductionism and well-ordering
___ (a) Zermelo's 1904 proof
___ (b) Inclusion orderings and the 1908 proof
__ 7.4 The problem of definite properties
8. Von Neumann's reinstatement of the ordinal theory of sets
__ 8.1 The von Neumann theory of ordinals
__ 8.2 The discovery of the replacement axiom
__ 8.3 Limitation of size revisited
Conclusion
Bibliography
Name index
Subject index

7 of 7 people found the following review helpful.
By far the BEST book on the development of Cantor's ideas.
By William D. Fusfield
This is BY FAR the best and most INTERESTING book available on how Cantor developed his key ideas about transfinite sets, large cardinals, ordinals etc. It contains materials that will be highly relevant to even the most advanced set theorists, while yet managing to be generally accessible to those who, like myself, have only around a B.S. mathematics degree level of understanding of the field. This ability to be of use and interest to readers with such widely varied mathematical preparations is a true tribute to the author's gift for being able to explain even very advanced concepts clearly and directly, something which is evident throughout the text, -- and unfortunately sorely missing in most mathematical texts operating at such a high level of abstraction. To be a bit more precise, I hope, persons with only a basic understanding of set theory -- something around what one should be able to glean from reading, say, Halmos' "Naive Set Theory" -- will indeed find themselves "out at sea" at times, but actually surprisingly FEW times, considering how well the author manages to unpack most of the key concepts and draw you back into the primary narrative. No doubt because this book is so much better than all its competitors, used copies, even the paperbacks, are now selling for a small fortune. [I kid you not, I just saw one listed at over $990!; though a few minutes of searching the main web book seller consolidators -- including the listings here at Amazon -- should still bag you one for under $100, at least if you act reasonably soon.] Clearly the publisher really needs to reissue this work to meet the fully justified demand! When and if they will do so, -- after all, it was last released, in its one and only paperback edition, in 1986! -- is anybody's guess. So, if you are a Cantor scholar, or a serious set theorist of any persuasion, you should probably bite the bullet and buy one now before the price really goes through the roof and you have to rely on marked-up, slowly disappearing library copies, -- until, that is, they all get stolen and resold on the web, which has happened to several classic math works already. One last thing, for those who don't really need the most sophisticated work on Cantor's intellectual development, Joseph Dauben's biography of Cantor is also very good and still widely available at a reasonable price. [His biography of Abraham Robinson is also very good by the way.]

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• Sales Rank: #3630526 in Books
• Published on: 1998-07-01
• Original language: English
• Number of items: 1
• Dimensions: 11.02" h x .20" w x 8.27" l, .61 pounds
• Binding: Paperback
• 74 pages

About the Author
Laura Echols-Richter is a full-time lay professional. Along with her husband, she serves on the staff of St. Andrew United Methodist Church in Plano, Texas. With over 15 years of youth ministry experience, Laura is an expert and brings her expertise to the faculty of Perkins School of Youth Ministry.

Billy Richter is an ordained United Methodist minister and has over 15 years of youth ministry experience. He is currently on staff at St. Andrew United Methodist Church in Plano, Texas. Billy is also on the faculty of Perkins School of Youth Ministry.

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Excellent source book
By J. Cross
Excellent source book! Can be used over and over as there are many different programs inside. Can be used with adults.

1 of 2 people found the following review helpful.
From Abingdon Press:
By S. McDonald
Help youth find true meaning in the Christmas season! Through these exciting programs and meaningful practices, youth will meet Jesus in a personal way. Each program has a related practice, which gives youth the opportunity to experience various traditions and celebrations related to the season. In addition, readers will find a photocopiable weekly newsletter with devotional and bible study materials and journaling exercises to encourage youth in their spiritual life and in their attendance. Use all programs and practices or pick and choose to fit specific needs.

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lAURA'S BOOK
By Donald L. Sielert
SHE AND BILLY ARE OUR MINISTER'S AND THEY ARE TERRIFIC. I GOT THIS FOR OUR DAUGHTER WHO HELPS WITH TEACHING SUNDAY SCHOOL, AND THOUGHT THAT THIS WOULD BE A GOOD AIDE FOR THEM DURING THE ADVENT SEASON. SHE ALSO HAS 2 KIDS--AGE 9 AND 10 SO THIS IS GOING TO BE PERFECT FOR THEM.

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Incredible things happen when you give up control.

As a young wife and mom-to-be, Joni Lamb never imagined a dream and Duct tape could launch a growing television network and career as host of two programs that reach millions of viewers worldwide every day with help, hope, and wisdom. Then a simple act of surrender to God helped her use ordinary things to achieve her extraordinary dreams.

That same simple act can help you find unshakeable peace, incredible power, and confident purpose too. Surrender All contains practical know-how and Joni’s remarkable story of how giving up control to God can…

• deepen every relationship,
• buoy any career,
• strengthen all finances,
• restore your health;
• get you through great loss or failure.

Drawing upon her experiences as a wife, mother, and television personality, Joni also shares the inspiring stories of others, celebrities and everyday folk, who found fresh hope in difficult circumstances by surrendering all:

• the couple whose marriage was fully restored–two years after their divorce,
• the mother whose faithful prayers for her drug-dealing son received an unexpected answer,
• the romance novelist who surrendered her career and found a whole new level of success,
• and the renowned sportscaster whose alcohol addiction nearly destroyed his life…until he chose to believe that God had greater plans for his future.

You can step confidently into your own divinely-designed destiny, Joni’s story reveals; she comes alongside to show you the way to making real the dreams of a heart willing to Surrender All.


From the Hardcover edition.

• Sales Rank: #731982 in eBooks
• Published on: 2008-09-16
• Released on: 2008-09-16
• Format: Kindle eBook

Review
“Joni Lamb proves that surrendering all to the Lord ultimately results in unlimited happiness, peace, health, joy, success, and love beyond all comprehension. Surrender All is inspirational! A blessing! A must-read!”
–Gavin MacLeod, actor and author of Back on Course

“Joni Lamb speaks to the heart. Her uplifting, motivating message will show you just how simple and powerful surrender to God is–how surrender can turn hopelessness to purpose and helplessness to power. By surrendering all, your doubts will be replaced by confidence, your fears diminished by strength, and your desires turned to dreams-that-can-come-true.”
–Bishop T.D. Jakes, senior pastor of The Potter’s House of Dallas

“Surrender All is a book to be savored and saved. During a trying time in my life, Joni’s words and the stories blessed me and reminded me that I can trust the Lord with everything. I can continue to cling to Proverbs 3:5-6. I know this book will greatly encourage everyone who reads it, and I hope thousands will!”
–Francine Rivers, author of Redeeming Love

“Joni Lamb writes with believable truth and testimony, ignited by the fact that she has learned and lives out the message she delivers here–Surrender All!”
–Jack W. Hayford, president of The International Foursquare Church and Chancellor of The King’s Seminary


From the Hardcover edition.

Review
“Joni Lamb proves that surrendering all to the Lord ultimately results in unlimited happiness, peace, health, joy, success, and love beyond all comprehension. Surrender All is inspirational! A blessing! A must-read!”
–Gavin MacLeod, actor and author of Back on Course

“Joni Lamb speaks to the heart. Her uplifting, motivating message will show you just how simple and powerful surrender to God is–how surrender can turn hopelessness to purpose and helplessness to power. By surrendering all, your doubts will be replaced by confidence, your fears diminished by strength, and your desires turned to dreams-that-can-come-true.”
–Bishop T.D. Jakes, senior pastor of The Potter’s House of Dallas

“Surrender All is a book to be savored and saved. During a trying time in my life, Joni’s words and the stories blessed me and reminded me that I can trust the Lord with everything. I can continue to cling to Proverbs 3:5-6. I know this book will greatly encourage everyone who reads it, and I hope thousands will!”
–Francine Rivers, author of Redeeming Love

“Joni Lamb writes with believable truth and testimony, ignited by the fact that she has learned and lives out the message she delivers here–Surrender All!”
–Jack W. Hayford, president of The International Foursquare Church and Chancellor of The King’s Seminary

About the Author
Joni Lamb is executive producer and co-host of Celebration, the daily flagship program of the Daystar Television Network, which she and husband Marcus, the network’s CEO, founded, built, and operate. The Lambs own more than 50 television stations reaching 75 million homes in the U.S. and every country across the globe, and theirs is the fastest-growing Christian television network in the world.

Joni also hosts the lively and sometimes unpredictable half-hour daily talk show bearing her name, which earned the National Religious Broadcast Association’s Best Talk Show Award in 2004. Broadcast twice daily, the Joni show features an array of notable guests and covers a wide range of relevant issues, controversial subjects, and hard-hitting news topics with candor and wit. Joni appeals to a broad, multicultural audience by focusing on the relevance of faith to every aspect of life.

The Lambs live in Dallas, Texas, and are the parents of three children: Jonathan, Rachel, and Rebecca. Their family ministers frequently throughout the country.

Most helpful customer reviews

4 of 5 people found the following review helpful.
Enjoyable read
By Robin Dabbs
I found this book to be a very easy read. I enjoyed it very much. Once I picked it up, I couldn't put it down. It's uplifting, warm, encouraging, and I would highly recommend it to others.
I'm looking for Joni's next book!

0 of 1 people found the following review helpful.
Surrender All
By Faye M. Lloyd
Surrender All is a well written book and it tell about the author and her family and many more on her TV show. Joni Lamb is a tremendous Christian wife and mother. I bought two of her books one for my daughter and one for me.

10 of 11 people found the following review helpful.
Quick, interesting read
By Lisa@SliceofLife
"Surrender All: Your Answer To Living with Peace, Power & Purpose" by Joni Lamb is a fairly quick, easy read that at times can come across as a little trite especially if you have recently suffered a type of crisis or tragedy in your life that she addresses in the book. However, just when you decide that she is oversimplifying some of life's greatest struggles, Mrs. Lamb will surprise you with a thought-provoking statement.

She discusses surrender in several areas of our lives such as marriage, children, career, and loss. Joni recounts dramatic, almost unbelievable at times, stories of extraordinary people who have had to surrender to God in the most difficult of circumstances. In fact, some of the stories she shares could have entire books written about them and really couldn't be covered in depth enough in this book which left me feeling as though she were a little bit flippant with them.

She also uses her own personal experience to share her uplifting, encouraging message of surrendering your all to God. Joni constantly reassures us that God will mend and restore all aspects of our lives including finances, health and relationships if we will just surrender them to Him. However, she is also very careful to make sure we understand that God hasn't promised us a life of ease as His children and that surrender doesn't guarantee a worry-free existence. Sometimes she flirts a little with the "prosperity gospel" or "name it and claim it theology" but mostly her advice seems to be grounded in Scripture. Most importantly, she makes sure to share the most significant story of surrender: Jesus.

Overall, Mrs. Lamb's book is an interesting read that should encourage you to examine your own life for areas that need surrender in order to bring about the peace you are longing for.

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In cooperation with the Plimoth Plantation, a living-history museum in Massachusetts, this book recreates the true story behind the first Thanksgiving in 1621, setting aside popular myths to present a fresh look at this historical event.

• Sales Rank: #4454748 in Books
• Published on: 2004
• Number of items: 2
• Binding: Paperback
• 47 pages

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