Mathematics and Philosophy (p)reprints of

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)from 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.


  • Formalization without Foundationalism: Model Theory and the Philosophy of Mathematical Practice Description and discount coupon pdf
  • 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

  •   Maximal models up the first measurable in ZFC ) pdf (rev. Dec. 2018)  with S. Shelah, A complete sentence in $L_{\omega_1,\omega}$ with maximal models cofinal in the first measurable is proved in ZFC

  •   Hanf numbers for Extendibility and related phenomena ) pdf (rev. Oct. 2018)  with S. Shelah, A complete sentence in $L_{\omega_1,\omega}$ with maximal models cofinal in the first measurable is consistent with ZFC+MC

  •   Henkin constructions of models with size continuum (submitted) (with M.C. Laskowski) pdf (first posted Oct 2018 but long in preparation   Survey and general method to build atomic models in the continuum

  •   The explanatory power of a new proof: Henkin's completeness proof (In M. Piazza and G. Pulcini, editors, Philosophy of Mathematics: Truth, Existence and Explanation, Boston Studies in the History and Philosophy of Science, 2017) pdf (rev. Feb 2017 first posted: Jan 2017)  Comparing completeness proofs

  •   Foundations of Mathematics: Reliability AND Clarity: the explanatory role of mathematical induction ) pdf (May 2016) What arguments by mathematical induction actually explain; WOLLICS 2016

  •   Hanf Numbers and Presentation Theorems in AEC (with W. Boney) pdf (In Jose Iovino, editor, Beyond First Order Model Theory, pages 81–106. Chapman Hall, 2017 first: October 2015)  The Hanf number of amalgamation, jep etc. is at most the first strongly compact

  •   A Complete $L_{\omega_1,\omega}$-sentence with maximal models in multiple cardinalities (with I. Souldatos) pdf revised Sep 2017 first post Aug 15)  Main tool for title theorem is a Scott sentence with arbitrarily large $(\kappa^+,\kappa)$ models

  •   Constructing many atomic models in $\aleph_1$ (with M.C. Laskowski, S. Shelah) pdf (Dec 2015: Journal of Symbolic Logic 2016. 81(3): 1142-1162)  Introduces a new notion of closure for atomic classes; estabishes the existence of dimension of many types from few models in $\aleph_1$ by passing through models of set theory to establish ZFC results

  •   The Joint Embedding Property and Maximal Models (with M. Koerwien,Ioannis Souldatos) pdf (Nov 2015 first Feb 2015 pub online Archive Math Logic March 28, 2016)  Examples of AEC with maximal models in various cardinalities but also arbitarily large models

  •   Axiomatizing Changing Conceptions of the geometric continuum I: Euclid-Hilbert pdf (Oct 2017: first Jan 2015) Philosophia Mathematica, nkx030,  What are the the goals of axiomatization? We introduce the notion of a modest descriptive axiomatization. All of Euclid is provable in first order logic (basically in Hilbert; talk for MWPMWS 15 Notre Dame, Oct.18, 2014.

      The published version (improved more by editing than most papers) is at pdf

  •   Axiomatizing Changing Conceptions of the Geometric Continuum II: Archimedes-Descarte-Hilbert-Tarski pdf (Oct 2017: first Jan 2015)Philosophia Mathematica, nkx031, Published: 23 November 2017  We extend Part I to formulas for circumference and area of circle using o-minimality and argue for the immodesty of Hilbert's axioms ; talk for MWPMWS 15 Notre Dame, Oct.18, 2014

      The published version (improved more by editing than most papers) is at pdf

  •   Disjoint amalgamation in locally finite AEC (with M. Koerwien, and C. Laskowski) pdf to appear JSL revised Apr 2016 first post Mar 2014 )  New definition of $(\leq,k)$ disjoint amalgamation; gives uniform $\phi_r$ that homogeneously characterizes $\aleph_r$. ap holds up to $\aleph_{r-2}$ and in $\aleph_r$ but fails in $\aleph_{r_1}. Excellence without stability

  •   Three Red Herrings around Vaught's conjecture ( with S. Friedman, M. Koerwien, and C. Laskowski pdf   a) Eliminate the theory from Hjorth's theorem on uncountable models of a Vaught counterexample; b) strengthen the conclusion from no model in $\aleph_2$ to every model in $\aleph_1$ is maximal, c) give new argument for Harrington's theorem that a Vaught counterexample has models in $\aleph_1$ of arbitrary Scott rank (Sept 2014 version: to appear Transactions of the American Mathematical Society)

  •   From Geometry to Algebra pdf (Oct 2013 version; a few typos fixed: June 2014)  How much of Hilbert's axiomatization of geometry goes beyond first order? Multiplication is not repeated addition! Paper presented Oct 3, 2013 at philosophy of Math Practice Conference Urbana

  •   Iterated elementary embeddings and the model theory of infinitary logic (with Paul Larson) pdf (August 2015 version)  Use ultralimits of models of set theory to prove results on models in $\aleph_1$ of infinitary sentences (to appear APAL)

  •   Almost Galois omega-stability (with Paul Larson and Saharon Shelah) pdf (March 2015 version)  Assuming few models in $\aleph_1$, Almost Galois omega-stability implies Galois omega stability. to appear JSL
  •   Completeness and Categoricity (in power): Formalization without Foundationalism pdf (revised Nov. 2013) The Bulletin of Symbolic Logic / Volume 20 / Issue 01 / March 2014, pp 39-79; Presented at Midwest Philosophy of Mathematics Workshop (Oct. 27, 2012), Logic Day University of Chicago (Apr 2013), Carol Wood festschrift June 1,2013). 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

    `Bill Howard's recollection of contacts between logicians and Bourbaki' July 2013 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 II Superstable case pdf Math Logic Quarterly, Volume 60, Issue 6, pages 437–443, November 2014)  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. Volume 39, Issue 1, March 2013, Page 1-26
  •   Beyond First Order Logic: From number of structures to structure of numbers: Part 2 (with Tapani Hytinnen and Meeri pdf (June 2011 version: Bulletin of Iranian Math Soc. MARCH 2013 , Volume 39 , Number 1; Page(s) 27 To 48)  (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


  •   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 July 2013: \underline{Logic Without Borders} (2015) Ed. by Hirvonen,Asa / Kontinen, Juha / Kossak, Roman / Villaveces, Andres pp. 31-50) pdf


  •   A Hanf number for saturation and omission —   (with Saharon Shelah);  pdf
  • ( Fund. Math. 213 (2011))


  •   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:Journal of Mathematical Logic Volume 12, Issue 01, June 2012)

  •   Review of The Birth of Model Theory by Calixto Badesa —   This is a Halmos-style Bull. Amer. Math. Soc. 47 (2010), 177-185. 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 ShelahJ. Symbolic Logic Volume 74, Issue 3 (2009), 914-928.
  • 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: Annals of Pure and App. Logic 149 (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: to appear JSL) 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)
  •   Some Projective Planes of Lenz-Barlotti Class I pdf Proceedings AMS (123) 1995 251-256)  originally Fall 2012
  • The remainder are postscript files. to JohnBaldwin'sHome Page