MARC Record from marc_columbia

LEADER: 04069cam a2200349 a 4500
001 7284732
005 20221130224845.0
008 090506s2009 riu b 001 0 eng
010 $a 2009018740
020 $a9780821848937 (alk. paper)
020 $a0821848933 (alk. paper)
035 $a(OCoLC)ocn320621732
035 $a(NNC)7284732
035 $a7284732
040 $aDLC$cDLC$dNNC$dOrLoB-B
050 00 $aQA9.67$b.B35 2009
082 00 $a511.3$222
100 1 $aBaldwin, John T.$0http://id.loc.gov/authorities/names/n86039426
245 10 $aCategoricity /$cJohn T. Baldwin.
260 $aProvidence, R.I. :$bAmerican Mathematical Society,$c2009.
263 $a0908
300 $axi, 235 pages ;$c26 cm.
336 $atext$btxt$2rdacontent
337 $aunmediated$bn$2rdamedia
490 1 $aUniversity lecture series ;$vv. 50
504 $aIncludes bibliographical references and index.
505 00 $gPt. 1.$tQuasiminimal Excellence and Complex Exponentiation -- $gCh. 1.$tCombinatorial Geometries and Infinitary Logics -- $gCh. 2.$tAbstract Quasiminimality -- $gCh. 3.$tCovers of the Multiplicative Group of C -- $gPt. 2.$tAbstract Elementary Classes -- $gCh. 4.$tAbstract Elementary Classes -- $gCh. 5.$tTwo Basic Results about L[subscript w1,w](Q) -- $gCh. 6.$tCategoricity Implies Completeness -- $gPt. 3.$tAbstract Elementary Classes with Arbitrarily Large Models -- $gCh. 8.$tGalois types, Saturation, and Stability -- $gCh. 9.$tBrimful Models -- $gCh. 10.$tSpecial, Limit and Saturated Models -- $gCh. 11.$tLocality and Tameness -- $gCh. 12.$tSplitting and Minimality -- $gCh. 13.$tUpward Categoricity Transfer -- $gCh. 14.$tOmitting Types and Downward Categoricity -- $gCh. 15.$tUnions of Saturated Models -- $gCh. 16.$tLife without Amalgamation -- $gCh. 17.$tAmalgamation and Few Models -- $gPt. 4.$tCategoricity in L[subscript w1, w] -- $gCh. 18.$tAtomic AEC -- $gCh. 19.$tIndependence in w-stable Classes -- $gCh. 20.$tGood Systems -- $gCh. 21.$tExcellence Goes Up -- $gCh. 22.$tVery Few Models Implies Excellence -- $gCh. 23.$tVery Few Models Implies Amalgamation over Pairs -- $gCh. 24.$tExcellence and *-Excellence -- $gCh. 25.$tQuasiminimal Sets and Categoricity Transfer -- $gCh. 26.$tDemystifying Non-excellence -- $gAppendix A.$tMorley's Omitting Types Theorem -- $gAppendix B.$tOmitting Types in Uncountable Models -- $gAppendix C.$tWeak Diamonds -- $gAppendix D.$tProblems.
520 1 $a"Modern model theory began with Morley's categoricity theorem: A countable first-order theory that has a unique (up to isomorphism) model in one uncountable cardinal (i.e., is categorical in cardinality) if and only if the same holds in all uncountable cardinals. Over the last 35 years Shelah made great strides in extending this result to infinitary logic, where the basic tool of compactness fails. He invented the notion of an Abstract Elementary Class to give a unifying semantic account of theories in first-order, infinitary logic and with some generalized quantifiers. Zilber developed similar techniques of infinitary model theory to study complex exponentiation." "This book provides the first unified and systematic exposition of this work. The many examples stretch from pure model theory to module theory and covers of Abelian varieties. Assuming only a first course in model theory, the book expounds eventual categoricity results (for classes with amalgamation) and categoricity in excellent classes. Such crucial tools as Ehrenfeucht-Mostowski models, Galois types, tameness, omitting-types theorems, multi-dimensional amalgamation, atomic types, good sets, weak diamonds, and excellent classes are developed completely and methodically. The (occasional) reliance on extensions of basic set theory is clearly laid out. The book concludes with a set of open problems."--BOOK JACKET.
650 0 $aCompleteness theorem.$0http://id.loc.gov/authorities/subjects/sh85029362
650 0 $aModel theory.$0http://id.loc.gov/authorities/subjects/sh85086421
830 0 $aUniversity lecture series ;$vv. 50.
852 00 $bmat$hQA9.67$i.B35 2009g