Boolean-Valued Models and Independence Proofs in Set Theory (Oxford Logic Guides)

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THE book for studying Boolean-valued models of set theory.......2001-08-15

If you are studying to become a set theorist these days (2001 or later), you will probably learn forcing by way of partial orders. This is the quickest way to go, and for most purposes, the most useful in applications. It's also the approach that is taken in Kunen's book on set theory, which is still pretty much the standard textbook.

Nonetheless, you may one day find that you need the Boolean algebra approach. This was the approach developed by Scott and Solovay after Cohen's somewhat inscrutable approach to proving the consistency of not-CH had been adequately digested. The Boolean algebra approach is very elegant and algebraic, and the theorems are often better motivated than they are in the partial orders approach.

When I was a graduate student, I studied both approaches, but eventually forgot much of what I learned about Boolean-valued models because in practice I always relied on the other approach.

Recently, however, in some research I've been doing in an extension of ZFC in an extended language, I found that some of the usual assumptions one can make in doing forcing over ZFC models were no longer applicable in the new setting. Without going into the details, the consequence was that I had to do forcing over non-wellfounded models of ZFC and examine the properties of the resulting forcing extension, perhaps iterating the process omega many times. The only way to do this has been to work with Boolean-valued models M^B of the non-wellfounded ground model M, prove the desired properties within M^B, then collapse with a generic ultrafilter, and go on to the next model.

Well, after that long-winded introduction, my point is this: Bell's treatment of Boolean-valued models is outstanding. I have several of Bell's books and his talent as an expositor is his relentless attention to detail. He does no hand-waving. If you need to face the details of Boolean-valued models, Bell's approach is the right way to go.

In the first chapter he develops the theory enough to prove that all ZFC axioms hold in V^B. In Chapter 2 he shows how to do independence proofs in Boolean valued models -- illustrating with CH and developing the usual results about chain conditions and distributivity, never once working with a 2-valued forcing extension. The third chapter reveals some of the elegance of the Boolean algebra approach in its development of the proof of the consistency of not-AC using group actions. Chapter 4 shows how to get the usual results about forcing involving 2-valued models by considering (V^B)/U, where U is a generic ultrafilter. Chapter 5 is a special chapter about cardinal collapsing, introduced because the Boolean algebras introduced before always preserved cardinals and cofinalities. Finally, chapter 6, which was added in the 1985 edition, treats iterated forcing. This chapter contains details that appear nowhere else and are very handy if you need to deal with such things.

Book Description

"Contains a balanced account of recent advances in set theory, model theory, algebraic logic, and proof theory, originally presented at the Tenth Latin American Symposium on Mathematical Logic held in Bogata, Columbia. Traces new interactions among logic, mathematics, and computer science. Features original research from over 30 well-known experts worldwide."

Models, Algebras, and Proofs: Selected Papers of the Tenth Latin Ameri

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Models, Algebras, and Proofs: Selected Papers of the Tenth Latin Ameri
Xavier Caicedo
Manufacturer: Publisher Unknown
ProductGroup: Book
Binding: Paperback
ASIN: B000UYFQ64

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Models, Algebras, and Proofs: Selected Papers of the Tenth Latin Ameri
Xavier Caicedo
Manufacturer: see notes for publisher info
ProductGroup: Book
Binding: Paperback
ASIN: B000M4NZM4

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From the incredible wizardry of Merlin to the undeniable passion of Sir Launcelot, these tales of Arthur and his knights offer epic adventures with the supernatural-as well as timeless battles with our own humanity.

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The legends of King Arthur and his knights of the Round Table have inspired some of the greatest works of literature--from Cervantes's Don Quixote to Tennyson's Idylls of the King. Although many versions exist, Malory's stands as the classic rendition. Malory wrote the book while in Newgate Prison during the last three years of his life; it was published some fourteen years later, in 1485, by William Caxton. The tales, steeped in the magic of Merlin, the powerful cords of the chivalric code, and the age-old dramas of love and death, resound across the centuries.

Customer Reviews:

Free SF Reader.......2007-09-03

I have to say it took me quite a few sausage roll lunch hours to get through this one as a kid. There is no doubt it is very interesting and important for the whole Arthur thing.

Those interested should definitely check it out from that point of view, even if only having a browse, it is well worth the time to see the origins of a lot of this.

A classic.......2007-08-24

What a delight. I read this book as a child [over 50 years ago] and it was a wonderful trip back in time for me to read it again. I had forgotten how well produced and written it was. This Malory version captures the spirit of the era.

Well worth purchasing.

You need it if you are going to read Vol II.......2007-07-08

I purchased this book because my husband owns vol II and wanted to read vol I first. If you love epics, masonry, legends, and the like this is the book for you.

Keith Baines's Modern Version.......2007-06-29

Aamazon has lumped together reviews of most available versions and editions of Malory's classic, and it isn't always possible to tell just which one a reviewer is talking about. This review applies solely to the Signet Classic modern-English version by Keith Baines.

Sir Thomas Malory's "Le Morte D'Arthur" was published in 1485. That was at the very end of the Middle English period. What that means is that the ERnglish that Malory spoke was in many ways closer to Chaucer's than to our own. You can read the original, but you'll need an extensive glossary and a good deal of practice.

Nearly fifty years ago Keith Baines took the somewhat daring step of presenting Malory's proto-novel in Modern English. Baines called his work a "rendition" rather than a "translation" because he has cut out a fair amount of repetition and done a good deal of paraphrasing as well. Nevertheless, the resulting edition faithfully sets out all of the substance and most of the detail of the original in straightforward Modern English. There are no archaic "thees" and "thous," for example, yet, fortunately, Baines makes no attempt to "modernize" the level of diction. His prose therefore sounds appropriately sober without being stilted.

I read the Baines version in high school when there was no way I could have handled Malory's original Middle English. I loved it. Scholars are appropriately annoyed that Baines may have condensed a little too much, but if you're curious enough to delve deeper there's always Janet Cowan's Penguin Classic edition, which just modernizes the spelling, and the Norton edition which meticulously reprints the original and includes a number of academic essays to boot.

By the way, Malory's 1485 narrative of the Arthurian legend is quite a bit different in almost every way from T.H. White's deservedly popular and very humorous "Once and Future King." For one thing, Malory wasn't kidding around. His enduring classic of world literature is serious though filled with wonders. If you're mainly interested in the story, the Baines "rendition" is the best version of "Le Morte D'Arthur" available. (But take the fascinating introduction by poet Robert Graves, author of "Goodbye to All That" and "The White Goddess," with several grains of salt.)

Just the text, ma'am.......2007-01-08

This Modern Library edition runs true to form, lacking much in the way of supplemental material or notes but providing a good basic presentation of the text on quality paper in a good binding. An edition to keep on the shelf for occasional reading rather than a student's book. If there's a really good scholarly edition of the "Morte" out there I don't know about it - anyone?

Forging Chivalric Communities in Malory's Le Morte Darthur (Studies in Arthurian and Courtly Cultures)

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Forging Chivalric Communities in Malory's Le Morte Darthur (Studies in Arthurian and Courtly Cultures)
Kenneth Hodges
Manufacturer: Palgrave Macmillan
ProductGroup: Book
Binding: Hardcover

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ASIN: 1403967601
Release Date: 2005-05-12

Book Description

Forging Chivalric Communities examines how Malory presents chivalry as a dynamic code shaped by communities large and small for their own purposes, from the national effort of England to free itself of the Roman legacy to Trystram's energy as a champion of Cornwall, to women's efforts to include themselves in the chivalric world. Hodges shows that Malory treats chivalry not as a static institution but rather, as a dynamic, continually evolving ideal. Le Morte D'arthur is structured to trace how communities and individuals adapt or create chivalric codes for their own purposes; in turn, Hodges asserts, codes of chivalry shape groups and their customs.

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Great reading

Le Morte D'Arthur
Thomas Malory , and Derek Jacobi
Manufacturer: Highbridge Audio
ProductGroup: Book
Binding: Audio CD

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ASIN: 156511938X

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For over 1,000 years, tales of King Arthur and his Knights of the Round Table have enthralled people, among them Henry VIII and T.E. Lawrence. Proof of the Arthurian legend's timeless appeal is the fact that scarcely a year goes by without a new adaptation. Published in 1485, Sir Thomas Malory's epic poem Le Morte d'Arthur became the standard source for future Arthurian works such as Idylls of the King by Lord Tennyson and T.H. White's The Once and Future King. With its expressive, vigorous dialogue, Le Morte d'Arthur resounds with colloquial liveliness and ceremonious dignity, the style for a 15th-century gentleman. The audio recording grips the listener with the fascinating, fateful story of Arthur's ascension to the throne as a boy, his marriage to Guenevere, the formation of the Round Table Knights, the quest for the Holy Grail, the ill-fated passion between Lancelot and Guenevere, the treachery of Arthur's illegitimate son Mordred, and the ultimate destruction of Arthur's realm. A superb story of adventure, love, honor, and betrayal, Le Morte d'Arthur is filled with dramatic power and deep, tragic irony.

Customer Reviews:

Great reading.......2006-01-06

Derek Jacobi is as great a reader as he is an actor (listen, for example, to his readings of the Odyssey, or The Voyage of the Dawn Treader). One hopes that as age diminishes his acting, he will fill his time with many such readings. His rendition of Malory is perfect, and helps the modern listener to appreciate the gems of language embedded within Malory's not always sensible tales. A neglected classic brought to life.

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The once and future king...
Truly Legendary
yech

Le Morte D'Arthur
Keith Baines
Manufacturer: Random House Value Publishing
ProductGroup: Book
Binding: Hardcover

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Customer Reviews:

The once and future king..........2004-07-08

Sir Thomas Mallory was a great one to write the adventures of King Arthur and his knights - a knight himself, he led a life of intrigue and adventure, albeit not one that always lived up to the ideas of chivalry he penned at the heart of the Arthurian legends. Mallory did not invent Arthur; he is one of the principle medieval chroniclers, having time (he was in prison with nothing else to do, after all) to set down in prose stories he'd heard throughout his life. These were popular tales, not always told in the same way with the same details, as is true of most oral legends and transmitted stories, much to the later frustration of scholars and readers. The earliest printing of Mallory's stories had his authorship suppressed by Caxton, one of the better-known publishers of the time.

The earliest Arthurian legends date back as far as the late Roman times in Britain. Controversies abound, but many have settled on a late Roman or Romano-British general named Arturius - however, given the linguistic nature of the name (it is derivative of ruler or leader), it is impossible to know if this was in fact a name or a title, and the legends may be compilations of the acts of many leaders bearing the name. There was also a Welsh leader with the name/title Arddu, `Dark One', who is sometimes conflated into Arthurian legend. Arthur was celebrated in the pre-Norman times for the order and stability he represented; Arthur was celebrated in post-Norman times for his campaigns against Saxons. Arthur continues to be an intriguing character, today reminiscent of ancient mysteries as well as pagan and new age ideas as well.

In any event, Mallory doesn't attach specific dates to his tales. The book actually consists of many tales. The first is entitled `The Tale of King Arthur', which introduces the figures of Merlin, Gawain, Uwayne, Pellinore, Morgan le Fay (the Celtic war goddess Morgana, dressed up as Arthur's sister) and others, and includes the sword-in-the-stone event. While this text has been modernised by Keith Baines, there are certain crucial lines left in Mallory's English, including this most famous one:

Whoso pulleth oute this swerd of this stone and anvyld is rightwys kynge borne of all Brytaygne

Following this tale, Mallory includes many of the famous tales in Arthurian legend as stories more or less complete in themselves, but still linking to the other tales. `The Tale of Sir Lancelot du Lake' is a knight's tale indeed, with no fewer than twenty horseback duels back-to-back. `The Tale of Sir Gareth' is a similar spirited tale, less well known. `The Book of Sir Tristram of Lyoness' makes Tristram and Iseult, famous by other writers as well, into lovers, this time with a more happy ending than usual. The lesser known `Tale of Arthur and Lucius' describes battles and skirmishes with the emperor, but never really captured popular imagination.

Mallory saves the best for last, with three major tales - `The Tale of the Sangreal', the Holy Grail; `The Book of Sir Launcelot and Queen Gwynevere'; and finally, `Le Morte D'Arthur'. The tale of the Holy Grail continues into the present day in various fashions; here is contains strange glosses of the Old and New Testaments, as well as a good number of miracles, as one would expect from the Grail. The last tale, the death of Arthur, is probably the most famous, and the best written.

Even though an English knight, the courtly fashion was after a French design for many centuries after the Norman conquest, and this French influence in notable in the stories, from their titles to their plots and characterisations, including the places Mallory uses.

Keith Baines eliminates a lot of needless dialogue from his rendering here, but keeps the plot lines and sequence of action with integrity from earlier manuscripts and recited tales. His translation compares favourably with others, becoming a fairly standard text for good reason. Robert Graves (of `I Claudius' fame) provides an appreciative introduction to the text. Baines himself was a poet; however, this text, accepted somewhat reluctantly, is probably his best known work.

Arthur lives on into the modern world and beyond. Baines' edition gives it life to carry on.

Truly Legendary.......2002-04-29

Contained within the pages of this book, is the most notorious of all stories to emerge from the depths of the Dark Ages of European history. Sir Thomas Malory's Le Morte d'Arthur is quite possibly the greatest work of English literature and the source of the Arthurian legends, as we know them today. This legendary tale of King Arthur and the Knights of the Round Table is an exquisite story of adventure, love, honor, and betrayal. Throughout the whole of Malory's story there is the underlying theme that a thing's making is ultimately it's undoing, be it kingdom, man, or quest. Not only is this theme evident in this story but in his own life as well. Le Morte d'Arthur is a truly legendary work of art, given new life in this splendid rendition by Keith Bains.

yech.......2001-12-13

This book was terrible. By far one of the worst books I've ever read. The story is bland and he manages to make even the greatest tales of arthur boring.

Beardsley's Le Morte Darthur: Selected Illustrations (The Dover Art Library)

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Beardsley's Le Morte Darthur: Selected Illustrations (The Dover Art Library)
Aubrey Beardsley
Manufacturer: Dover Publications
ProductGroup: Book
Binding: Paperback

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ASIN: 0486417956

Book Description

Beardsley's illustrations for the Dent edition of the great Thomas Malory classic made him famous virtually overnight. This volume contains a rich selection of those splendid drawings, including floral and foliated openings, fauns and satyrs, initials, ornaments, and much more. Characters from Arthurian legend are portrayed in splendid full-page illustrations. 62 black-and-white illustration.

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Le Morte D'Arthur - Volume I
Thomas Malory
Manufacturer: Hyperion
ProductGroup: Book
Binding: Paperback

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ASIN: 1401307809

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Malory's le Morte D'arthur

Manufacturer: Mentor
ProductGroup: Book
Binding: Mass Market Paperback
ASIN: B000DCNDR2

Le morte d'Arthur, (Everyman's library, Romance. [no. 45, 46])

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Le morte d'Arthur, (Everyman's library, Romance. [no. 45, 46])
Thomas Malory
Manufacturer: E.P. Dutton & Co
ProductGroup: Book
Binding: Unknown Binding

Beardsleys Illustrations for Le Morte D'Arthur

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Early Beardsley

Beardsleys Illustrations for Le Morte D'Arthur
Aubrey Vincent Beardsley
Manufacturer: Dover Publications
ProductGroup: Book
Binding: Paperback

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ASIN: 0486223485

Customer Reviews:

Early Beardsley .......2004-11-24

This is a remarkable work. First, it is Beardsley's earliest commission, illustrations for Malory's classic. For that reason alone, it will interest fans of Beardsley's drawings.

Second, and what really fascinates me, is that Beardsley developed his drawing style visibly over the course of the 580+ works in this project. When I look at the drawings for the first few chapters, they seem harsh and angular (p.22 for example). In other samples (e.g. p.18-19), Beardsley uses textures to generate tonal effects. By the end of the book, his drawings are much closer to his more familiar style. The lines are more graceful, and there is less use of the middle tones - broad solid blacks and whites dominate.

This is certainly a book for the Beardsley fan. It is also a distinctive example for anyone unsure of what "an artist's development" refers to.

Just a small warning, though - this contains only fragments of the Malory text, and many of the drawings do not appear with the printing that defined their original context. This is about Beardsley's drawings, not about the book in which they appeared.

//wiredweird

The Birth, Life, and Acts of King Arthur ... And in the End Le Morte D'Arth ur ...

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The Birth, Life, and Acts of King Arthur ... And in the End Le Morte D'Arth ur ...
Aubrey] Malory, Sir Thomas [Beardsley
Manufacturer: Dorset Press
ProductGroup: Book
Binding: Hardcover
ASIN: B000KV3UAG

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