LEADER 03796nam 2200625Ia 450 001 9910812654603321 005 20200520144314.0 010 $a1-282-60793-6 010 $a9786612607936 010 $a1-4008-2618-7 024 7 $a10.1515/9781400826186 035 $a(CKB)2670000000028553 035 $a(EBL)537651 035 $a(OCoLC)700686802 035 $a(SSID)ssj0000433707 035 $a(PQKBManifestationID)11311337 035 $a(PQKBTitleCode)TC0000433707 035 $a(PQKBWorkID)10390903 035 $a(PQKB)10240773 035 $a(DE-B1597)446449 035 $a(OCoLC)1004871999 035 $a(DE-B1597)9781400826186 035 $a(Au-PeEL)EBL537651 035 $a(CaPaEBR)ebr10394777 035 $a(CaONFJC)MIL260793 035 $a(PPN)199244685 035 $a(FR-PaCSA)88838042 035 $a(MiAaPQ)EBC537651 035 $a(EXLCZ)992670000000028553 100 $a20030430d2004 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 14$aThe birth of model theory $eLowenheim's theorem in the frame of the theory of relatives /$fCalixto Badesa ; translated by Michael Maudsley ; revised by the author 205 $aCourse Book 210 $aPrinceton, N.J. ;$aOxford $cPrinceton University Press$dc2004 215 $a1 online resource (255 pages) 300 $aDescription based upon print version of record. 311 $a0-691-05853-9 320 $aIncludes bibliographical references and index. 327 $t Frontmatter -- $tContents -- $tPreface -- $tChapter 1. Algebra of Classes and Propositional Calculus -- $tChapter 2. The Theory of Relatives -- $tChapter 3. Changing the Order of Quantifiers -- $tChapter 4. The Löwenheim Normal Form -- $tChapter 5. Preliminaries to Löwenheim's Theorem -- $tChapter 6. Löwenheim's Theorem -- $tAppendix. First-Order Logic with Fleeing Indices -- $tReferences -- $tIndex 330 $aLöwenheim's theorem reflects a critical point in the history of mathematical logic, for it marks the birth of model theory--that is, the part of logic that concerns the relationship between formal theories and their models. However, while the original proofs of other, comparably significant theorems are well understood, this is not the case with Löwenheim's theorem. For example, the very result that scholars attribute to Löwenheim today is not the one that Skolem--a logician raised in the algebraic tradition, like Löwenheim--appears to have attributed to him. In The Birth of Model Theory, Calixto Badesa provides both the first sustained, book-length analysis of Löwenheim's proof and a detailed description of the theoretical framework--and, in particular, of the algebraic tradition--that made the theorem possible. Badesa's three main conclusions amount to a completely new interpretation of the proof, one that sharply contradicts the core of modern scholarship on the topic. First, Löwenheim did not use an infinitary language to prove his theorem; second, the functional interpretation of Löwenheim's normal form is anachronistic, and inappropriate for reconstructing the proof; and third, Löwenheim did not aim to prove the theorem's weakest version but the stronger version Skolem attributed to him. This book will be of considerable interest to historians of logic, logicians, philosophers of logic, and philosophers of mathematics. 606 $aLogic, Symbolic and mathematical 615 0$aLogic, Symbolic and mathematical. 676 $a511.3092 700 $aBadesa$b Calixto$0726359 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910812654603321 996 $aThe birth of model theory$94108193 997 $aUNINA