# John T. Baldwin

### If you click on the name of the paper and have an appropriatereader, itwill appear now. The newest papers are available in pdf format on this page. Some of the older postscript files can be obtained by anonymous ftp (loginname"anonymous" or "ftp"; password can beanything)fromftp://www.math.uic.edu/pub/preprints/baldwin/. You will need to uncompress these files with the command pkunzip or gunzip. In those cases, the name of the archived file is in parentheses.

• Categoricity in Abstract Elementary Classes 245 pages in AMS format: appeared August 2009 —   The printed version will cost $55. pdf • Categoricity in Abstract Elementary Classes ;Corrections to the monograph pdf • Iterated elementary embeddings and the model theory of infinitary logic (with Paul Larson) pdf (March 2012 version) Use ultralimits of models of set theory to prove results on models of aleph 1 of infinitary sentences • Almost Galois omega-stability (with Paul Larson and Saharon Shelah) pdf (July 2012 version) Assuming few models in aleph-1 Almost Galois omega-stability implies Galois omega stability • Completeness and Categoricity (in power): Formalization without Foundationalism pdf (April 2013) Presented at Midwest Philosophy of Mathematics Workshop (Oct. 27, 2012). Formal methods as a mathematical tool. • Vaught's fundamental paper Denumerable models of complete theories' is very difficult to find on line. I include it for convenience. pdf • Formalization, Primitive Concepts and Purity pdf (August 2012) text is philosophical', appendix with Bill Howard gives a geometric proof that every Desarguesian plane is embeddible in three space: Review of Symbolic Logic vol 6, 2013 • Saturation and Omission II Superstable case pdf (April 2013) originally Fall 2012 • Beyond First Order Logic: From number of structures to structure of numbers: Part I (with Tapani Hytinnen and Meeri pdf (June 2011) (Intro to AEC; the notion of completenesss; Bulletin of Iranian Math Soc. • Beyond First Order Logic: From number of structures to structure of numbers: Part 2 (with Tapani Hytinnen and Meeri pdf (June 2011 version) (Intro to AEC; the notion of completenesss; an amusing AEC from PA) • Geometry and Categoricity (July 5, 2010 version) pdf (for Kirishma volume; expanded from Zilber-fest talk. March 2010) • The next few items were preliminary musings towards Purity' and Formalism without foundations' above. Modern Model Theory\\ The impact on mathematics and philosophy, Model Theory and Philosophy – Paris June2010. pdf Bib for Modern Model Theory\\ The impact on mathematics and philosophy, Model Theory and Philosophy – Paris June2010. pdf The following two papers overlap but each contains some material not in the other. Model Theoretic Perspectives on the Philosophy of Mathematics— paper for the Workshop in Practice Based Philosophy - Amsterdam Aug 2009. pdf More philosophically oriented version. Model Theoretic Perspectives on the Philosophy of Mathematics— paper for the Workshop in Practice Based Philosophy - Amsterdam Aug 2009. Longer and more mathematical version pdf • A How big should the monster model be? ( Vä ä n ä nen Birthday party; Comparison of Grothendieck's and Shelah's approach to universal domains and problems arising in the study of unstable theories. Revised Apr. 2013) pdf • • A Hanf number for saturation and omission — (with Saharon Shelah); pdf • (April 2011 version to appear Fund. Math.) • Amalgamation, Absoluteness, and Categoricity — Southeast Asia Logic Conference, (version of Mar 2012: Appendix by David Marker-appeared) pdf • • Stability Spectrum for Classes of Atomic Models — (with Saharon Shelah); New results on stability spectrum and general discussion of EM models over trees of indiscernibles pdf • (March 2012 version: to appear JML June 2012) • Review of The Birth of Model Theory by Calixto Badesa — This is a Halmos-style review for the Bulletin of the AMS. If takes off from the book to sketch the history/viewpoint of model theory and its connections with core mathematics. pdf • A Field Guide to Hrushovski Constructions — This is an annotated bibliography with a few open problems to papers based on the Hrushovski construction. There are sections on the ab initio constructions, expansions/fusions, and infinitary versions. Although written as slides, the notes are compiled in printable form. Suggestions for updates are appreciated. pdf • The Amalgamation Spectrum posted Spring 2008: pdf with Alexei Kolesnikov and Saharon Shelah • Generalized Quantifiers, Infinitary Logics, and Abstract Elementary Classes posted Dec. 2007: pdf Proceedings of Mostowki conference July 2007 • N perp as an AEC (with Paul Ekof and Jan Trlifaj) posted Dec. 2006, revised June 2007: pdf • Categoricity, Amalgamation, and Tameness (with Alexei Kolesnikov) posted Oct. 2006, final version revised Nov 2007 to appear: Israel Journal of Math pdf • Geometry and Proof : Tools for Teaching Logic, Conference in Salamanca, September 2006 pdf • Cayley's theorem for ordered groups: o-minimality (with Bektur Baizhanov and Viktor Verbovskiy) pdf (posted August 2006) • The complex numbers and complex exponentiation: Why Infinitary Logic is necessary! (Annual Meeting of Columbian Mathematical Society: August 2005) pdf (posted April 2006) • The Vaught Conjecture, Do uncountable models count (February 2006 rev. July 2006) (For Vaught conjecture Conference held May 2005) pdf • Examples of Non-locality (with Saharon Shelah)(Fall 2005; revised Fall 2007: appeared JSL(73) 2008) pdf • Abstract Elementary Classes: Some Answers, More Questions (Logic Colloquium 2004, Turino) pdf (revised Summer 2006) • Uncountable Categoricity of Local Abstract Elementary Classes with Amalgamation (with Olivier Lessmann) (first post Spring 2005; revised Fall 2005; bib updated Apr 2006) pdf • The Metamathematics of Random Graphs (posted Spring 2005; revised Fall 2005) pdf • Upward stability transfer for Tame Abstract Elementary Classes(with David Kueker and Monica VanDieren) (Spring 2004) pdf • Non-splitting Extensions (Spring 2004) pdf technical report: Short proof to obtain nonsplitting extensions in EM models • Ehrenfeucht-Mostowski Models and Abstract Elementary Classes(Fall 2003) pdf • Review of Lavrov and Makismova: Problems in Set theory,Mathematical Logic and the Theory of Algorithms) pdf • Review of Wolfram's A New Kind of Science (Fall 2003) ps • Notes on Quasimiminality: Infinitary categoricity, complexexponentiation, Hrushovski Construction and Abstract ElementaryClasses(Spring 2004) pdf • Constructing$\omega$-stable Structures: Model Completeness (with Kitty Holland) (Summer 2003) postscript or dvi or pdf • Local Homogeneity (with Bektur Baizhanov) (Winter 2003; revisedSpring 2004) pdf • Subsets of Superstable Structures are weakly benign( with BekturBaizhanov and Saharon Shelah) (Winter 2003) pdf or dvi • CA Computation and Simulation (Note to FOM:Summer 2002) postscript dvi • Constructing$\omega$-stable Structures:Rank k fields ( withKitty Holland) (Summer 2002) postscript or dvi (Appeared NotreDame Journal of Formal Logic, (44) pg 139-147, 2003) • Forking and Multiplicity in First Order Theories (Spring 2001) postscript or dvi • Determined Theories and Limit Laws (with Marco Mazzucco) (Spring2001; revised Spring 2004) pdf • Model Companions of$T_\aut$for stable$T$(with Saharon Shelah)(Winter 2003) postscript or dvi • Rank and Homogeneity (Fall 2000) postscript or dvi • Amalgamation properties and finite models in$L^n$-theories (withOlivier Lessmann) (Summer 2000) postscript or dvi • Stable Amalgamation(expanded from Malcev conference) (January2000) (postscript) or dvi • Finite and Infinite Model Theory: a historicalperspective(expanded from Wollics conference) (Fall 1999) dvi or (postscript) • Constructing$\omega$-stable Structures:Computing Rank ( withKitty Holland) (summer 1999: rev Spring 2001) (dvi) or (postscript) • Theories in Finite Model Theory (April 1999: technicalreportIRCS, Philadelphia Workshop) (dvi) or (postscript) • Probability and the Finite Model Property:The "proof" thatHrushovski's example of an$\aleph_0$-categorical stable theory has thefinite model property has a serious error. (Later: Djordjevic found acounter example.) • Constructing$\omega$-stable structures:Rank 2 fields(with KittyHolland) (update: Spring 2001; original Mar. 98 below) (dvi version ) or (postscript) • Stability, the finite cover property, and$0$-$1\$ laws (March 8,1998) (dvi version) or (postscript)
• Stability theory, Permutations of Indiscernibles,and EmbeddedFinite Models ( with Michael Benedikt)(March 10, 1998)(dvi version) ) or postscript
• Random expansions of geometries (Accepted Jan 2003 version) (dvi version) or (postscript)
• Random expansions of geometries ( 1999 version) (dvi version) or (postscript)

The remainder are postscript files.