# 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)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.

** 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

**Reflections on De Zolt; Mathematical, Philosophical, and Historical**
pdf (January 2022) with Andreas Mueller; on the necessity of De Zolt's axiom
for the theory of area; International Conference on Modern Geometry and its Foundations Jan 15, 2022 14 pages
**Strongly minimal Steiner Systems III: Path graphs and sparse configurations**
pdf (November 2021) Adapting various combinatorial properties of Steiner
triple systems to strongly minimal $q$-Steiner systems 23 pages
**Towards a finer classification of Strongly minimal sets **
pdf (Sept 2021) Strongly minimal Steiner systems don't have definable binary functions; coauthor Viktor Verbovskiy, 58 pages
**Strongly Minimal Steiner Systems II: Coordinatization and Quasi-groups: **
pdf (Sept 2021) The strongly minimal Steiner
systems are coordinatized by quasigroups if line length is a prime power; but not definably
**Exploring the generous arena **
pdf (May 2021) Model theory and category theory as scaffolds for mathematics;
to appear in Maddy Volume
**The dividing line methodology:
Model theory motivating Set Theory**
pdf (Oct. 2020) survey of Shelah's work in set theory motivated by model theory; in honor of the
Schock prize; Theoria vol 87: 2 Feb 2021
**The autonomy of geometry **
pdf (Jan. 2020) On Van der Waerden, Hilbert, and Hartshorne;
coauthor Andreas Mueller; Annales Universitatis Paedagogicae Cracoviensis (2019)
**Images in Mathematics **
pdf (Jan. 2020) Conference Bogota, 2014 -- Theoria vol 87:4 2021
**The reasonable effectiveness of model theory in Mathematics **
pdf (Aug. 2019) survey of recent applications of model theory to combinatorics, machine learning;
connections with functional analysis and argument for why these connections should be expected;
Selected Topics from Contemporary Logic I, College Publications
**Strongly Minimal Steiner Systems I: Existence **
pdf (rev. Jan 21, 2020) to appear JSL; with G. Paolini, We construct strongly
minimal (2,k) Steiner systems for each k> 2
(counterexamples to Zilber's conjecture): more detail than submitted paper
**Maximal models up the first measurable in ZFC **
pdf (rev. Sep 2021) 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. Jan, 2021 ) with S. Shelah, A complete sentence in $L_{\omega_1,\omega}$
with maximal models cofinal in the first measurable is consistent with ZFC+MC; Archive for Math Logic, online October 13 2021
** Henkin constructions of models with size continuum (Bulletin of Symbolic Logic 2019)** (with M.C. Laskowski)
pdf 2018 Survey and general method to build atomic models in the continuum
** Finding $2^{\aleph_0}$ countable models for ordered theories
(Siberian Electronic Mathematical Reports 2018)** (with B. Baizhanov and T. Zambarnaya)
pdf (Slightly more general sufficient condition for an ordered theory to have the maximal number of countable models
**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 2019 MLQ, 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, https://doi.org/10.1093/philmat/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, https://doi.org/10.1093/philmat/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 JSL 2017 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
** Hanf number for Saturation and Omission 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.

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