Rami Grossberg
Department of
Mathematical Sciences
Carnegie
Mellon University
Ph.D. Hebrew University of Jerusalem, 1986 (advisor: Saharon Shelah )
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Recent papers |
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Teaching |
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Model Theory Seminar |
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Some links |
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Personal Information |
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Research |
I'm interested in model theory (a branch of logic), especially in the classification theory of non elementary classes, infinitary logics, extensions of first-order logic, combinatorial set theory, and the applications of these areas to algebra.
What Shelah think of model theory? See Saharon Shelah's short article
John Baldwin wrote a
paper
containing survey of results and some problems that occupy me in
recent years.
My old and outdated
"official" page in our departmental catalog is here.
Former graduate students and
their postdoctoral positions (in chronological order):
1.
Olivier Lessmann. Research
Assistant Professor at University
of Illinois at Chicago and EPSRC postdoc at Oxford University
PhD thesis: "Dependence relations in non elementary classes" pdf
157 pages. Won
the The
Hugh D. Young Graduate Student Teaching Award for 1996.
2.
Monica
VanDieren. Szego Assistant Professor at Stanford and
T.H.Hildebrandt Assistant Professor at the University of Michigan.
PhD thesis: "Categoricity and Stability in Abstract Elementary
Classes" pdf 130 pages.
3.
Alexei Kolesnikov.
Assistant Professor at University
of Michigan. PhD thesis: "Generalized amalgamation in Simple
theories and characterization of dependence in non-elementary classes" pdf 107
pages. Won
the Eberly teaching prize for 2001, the top university prize for graduate
students.
4.
Will Boney.
Benjamin Peirce Fellow and NSF Postdoctoral Fellow at Harvard University.
PhD thesis: "Advances in Classification Theory for Abstract Elementary
Classes" pdf 162 pages.
5.
Sebastien Vasey.
Benjamin Peirce Fellow at Harvard University. PhD thesis: "Superstability and
Categoricity in Abstract Elementary Classes" pdf 572 pages. The Guy C. Berry Graduate Student Research Award and The Sacks Prize
for 2017, for more information
6.
Marcos Mazari-Armida.
Burnett Meyer Postoctoral Fellow, University of Colorado, Boulder University of Colorado.
PhD thesis: "Remarks on classification theory for abstract elementary
classes with applications to abelian group theory and ring theory" pdf 259 pages. A recording of the thesis defense is made
available on June 17, 2021. Passcode: 7+yA.HRR
Won the Sacks Prize for 2021.
The Sacks Prize is awarded for the best dissertation of the year in logic. For more information
A nice article about the research of Marcos Mazari-Armida at the
Colorado Arts and Sciences Magazine
7. Hanif J. Cheung.
PhD thesis: "Notions of amalgamation for abstract elementary classes"
pdf 82 pages. A recording of the thesis defense is made
available on June 24, 2022. Passcode: 6v#EVfz=
Further information will be
posted by September.
8.
Samson Leung ,
Defended thesis on November 17th, 2022. Recording of the defense: https://cmu.zoom.us/rec/share/OmI-mx9ipyYpIuZOZ2Jlk7qLxzv3Exlf8uEZBtc1B1fPNOvFiISuatVzeGBjOt7i.RCYEHuhR_e4eJC6A
Passcode: Y3LYP&z# Won the departmental prize
for excellence in research for 2022 and the The Hugh D.
Young Graduate Student Teaching Award for 2022. STABILITY, CATEGORICITY AND AXIOMATIZATION OF
ABSTRACT ELEMENTARY CLASSES pdf
194 pages.
9.
Wentao Yang https://wen-tao-y.github.io
Researcher at Inner Mongolia University, China.
Defended in
April 2024. Thesis title: “On successive
categoricity, stability and NIP in abstract elementary classes”. 75 pages. Copy available from http://www.math.cmu.edu/~rami/Wentao.final_thesis.pdf
Current PhD students:
· Jeremy
Beard
· Jin Xi
Li
· Mick
Walker
Papers and theses written by PhD students while working under my guidance
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Recent papers |
Downloading files
in the DVI or PDF formats is much faster since they are only 30-40% of the size
of PS files. The files are optimized for PDF.
(c) All material accessible
through this page is copyright by Rami Grossberg and his coauthors and by the
corresponding publishers. Permission is granted for fair use in personal,
noncommercial, and academic projects.
1.
Rami
Grossberg and Saharon Shelah.
On universal locally finite groups, Israel Journal of Mathematics, 41, (1983)
289--302.
2.
Rami
Grossberg. Models with second order properties in successors of singulars,
Journal of Symbolic Logic, 54, (1989) 122--137. pdf file from JSTOR
3.
Rami
Grossberg and Saharon Shelah.
On the number of non isomorphic models of an infinitary theory which has the
order property Part A, Journal of Symbolic Logic, 51, (1986) 302--322. pdf file from JSTOR
4.
Rami
Grossberg and Saharon Shelah.
A non-structure theorem for a theory which has the unsuperstability property,
Illinois J. of Mathematics, 30, (1986) 364--390.
5.
Rami
Grossberg. A downward L\"{o}wenheim Skolem theorem for theories which have
the unsuperstability property, Journal of Symbolic Logic, 53, (1988) 231--242. pdf file from JSTOR
6.
Rami
Grossberg and Saharon Shelah.
On the structure of $Ext_p(G,{\bf Z})$, Journal of Algebra, 121, (1989)
117--128.
7.
Rami
Grossberg and Bradd Hart. The classification theory of excellent classes,
Journal of Symbolic Logic, 54, (1989) 1359--1381. pdf file from JSTOR
8.
Michael
Albert and Rami Grossberg. Rich models,
Journal of Symbolic Logic, 55, (1990) 1292--1298. pdf file from JSTOR
9.
Michael
Albert and Rami Grossberg. Characterizing
stability and superstability by unions of chains and saturated models, Research
Report No. 89-47, May 1989. pdf file
10.
Rami
Grossberg. Indiscernible sequences in a model which fails to have the order
property, Journal of Symbolic Logic, 56 (1991) 115--123. pdf file from JSTOR
11.
Rami Grossberg.
On chains of relatively saturated submodels of a model without the order
property, Journal of Symbolic Logic, 56, (1991) 123--128. pdf file from JSTOR
12.
Rami
Grossberg. Review of Wilfried Hodges's book -- "Building models by
games", Journal of Symbolic Logic, 56 (1991) 752--753. pdf file from JSTOR
13.
Martin Goldstern,
Rami Grossberg and Menachem
Kojman. Infinite homogeneous bipartite graphs with unequal sides,
Discrete Mathematics 149 (1996) 69-82. ps , dvi ,
pdf .
14.
Saharon Shelah
and Rami Grossberg. On cardinalities in quotients of inverse limits of
groups, Mathematica Japonica. 47 (1998), no. 2, 189-197. ps ,
dvi ,
pdf .
15.
John T. Baldwin,
Rami Grossberg and Saharon
Shelah. A characterization of the finite cover property and
stability, Journal of Symbolic Logic 64 (1999) 678-684. ps ,
dvi ,
pdf .
16.
Rami
Grossberg and Saharon Shelah.
On Hanf numbers of the infinitary order property. 19 pages, DRAFT
revised on 6/9/98. ps , dvi ,
pdf .
17.
Doug Ensley
and Rami Grossberg. Ramsey's theorem in stable structures, 37 pages,
last revision 8/4/1995. [Containing a start of forking via averages of
sequences in finite relational structures] pdf .
18.
Doug Ensley
and Rami Grossberg. Ramsey's theorem in stable structures, 21 pages, last
revision 5/15/97. [This is a truncated w/o model theory version of the above] ps ,
dvi ,
pdf .
19.
Rami
Grossberg and Olivier
Lessmann. Dependence Relation in Pregeometries, Algebra
Univesalis 44 (2000) pp 199-216. The published paper from Birkhauser's site. ps ,
dvi ,
https://www.math.cmu.edu/~rami/pregeo.pdf
20.
Rami
Grossberg and Olivier
Lessmann. The local order property in non elementary classes, Arch
Math Logic 39 (2000) 6, 439-457. The published paper from Springer's site. ps ,
dvi
, pdf .
21.
Rami
Grossberg, José
Iovino and Olivier Lessmann. A primer of simple theories, Archive
of Math Logic, 41, (2002), 541-580. The published paper from Springer's site. ps ,
dvi ,
pdf .
22.
Rami
Grossberg and Olivier
Lessmann. Shelah's stability spectrum and homogeneity spectrum in
finite diagrams, Arch. Math. Logic 41 (2002) 1, 1-31. The published paper from Springer's site. ps ,
dvi
, pdf .
23.
Rami
Grossberg. Classification theory for abstract elementary classes, Logic
and Algebra, ed. Yi Zhang, Contemporary Mathematics, Vol 302, AMS, (2002),
pp. 165--204. ps , https://www.math.cmu.edu/~rami/Rami-NBilgi.pdf
24.
Rami
Grossberg, Alexei
Kolesnikov, Ivan
Tomasic and Monica
VanDieren. The equality S1=D=R, Mathematical Logic Quaterly,
49, (2003), 115-128. pdf file from the publisher Wiley InterScience .
25.
Rami
Grossberg and Olivier
Lessmann. Abstract decomposition theorem and applications, Contemporary
Mathematics, Vol 380, (2005), AMS, pp. 73--108. ps ,
pdf .
26.
Rami
Grossberg and Monica VanDieren. Shelah's Categoricity Conjecture from
a successor for Tame Abstract Elementary Classes. Journal of Symbolic
Logic, Vol 71 (2006) 2, 553--568. ps ,
pdf .
27.
Rami
Grossberg and Monica VanDieren. Galois-stability for Tame Abstract
Elementary Classes. Journal of Mathematical Logic, Vol. 6, No. 1 (2006)
25--49. ps
, pdf .
28.
Rami
Grossberg and Monica VanDieren. Categoricity from one successor
cardinal in Tame Abstract Elementary Classes. Journal of Mathematical
Logic, Vol. 6, No. 2 (2006) 181--201. ps ,
pdf .
29.
Rami
Grossberg and Alexei
Kolesnikov. Superior Abstract Elementary Classes are Tame. 26
pages, last updated 9/9/05. ps ,
pdf .
submitted.
30.
Rami
Grossberg, Monica VanDieren and Andrés
Villaveces. Uniqueness of Limit Models in Classes with
Amalgamation. pdf
. Mathematical Logic Quarterly - Vol.62, Issue 4-5/2016, page
367-382.
31.
Will Boney
and Rami Grossberg. Forking in Short and Tame AECs. pdf . Ann. Pure Appl. Logic 168 (2017), no.
8, 1517--1551.
32.
Will Boney,
Rami Grossberg, Alexei
Kolesnikov and Sebastien Vasey. Canonical forking in AECs. pdf . Annals of Pure and Applied Logic 167 (2016), no. 7,
590--613.
33.
Rami
Grossberg, and Sebastien
Vasey. Equivalent definitions of superstability in tame abstract
elementary classes pdf . The Journal of Symbolic Logic 82 (2017), no. 4,
1387–1408. published
version
34.
Will Boney,
Rami Grossberg, Michael
Lieberman , Jiri Rosicky and Sebastien Vasey. $\mu$-Abstract elementary classes and
other generalizations. Journal of Pure and Applied Algebra 220 (2016), no.
9, 3048--3066. published version, pdf .
35.
Will Boney,
Rami Grossberg, Monica VanDieren and Sebastien Vasey. Superstability from categoricity in
AECs. pdf . Annals of Pure and Applied Logic 168 no. 7
(2017)1383--1395. published version
36.
Rami
Grossberg and Marcos Mazari-Armida . Simple-like independence
relations in abstract elementary classes, Annals of Pure and Applied Logic,
Volume 172, Issue 7, (2021), 28 pages pdf published
version
I am working on three volume model theory book series:
· A course in Model Theory I: Introduction, 815 pages.
· A course in Model Theory II: Classification Theory, 233
pages.
· A course in Model Theory III: Classification Theory for
Abstract Elementary Classes, 205 pages.
For more information click here .
Note on PDF: Some ligatures may not display correctly on your screen, depending on your operating system. However, the output on a PostScript printer should be of excellent quality.
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Teaching |
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Spring, 2020 |
Fall, 2020 |
Spring, 2021 |
Fall, 2021 |
Spring, 2022 |
Fall, 2022 |
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Model Theory Seminar |
Little before fall
1992 I started a Mathematical
Logic Seminar and managed it until fall 2002. I am not responsible
for that seminar anymore, it is run now in a different format than in the past
by Ernest Schimmerling.
At present I am organizing a Model
Theory Seminar. Since the pandemic started in Spring 2020 we meet
via zoom on Thursdays 11-12:30 PM. Before Covid we used to meet on Mondays
5-6:30PM in WeH 7201. We may return to this schedule in January 2023.
Information about current and past talks can be found here.
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Some links |
· This
semester Will
Boney is teaching in Harvard a course titeled Classification Theory for Tame Abstract Elementary Classes .
· Ariella: Most people think that girls can not excel at
engineering and math, but I dont care what they say, I am going to be an
engineer someday, From the Pittsburgh Post Gazette,
· A non-Erdos like interview with my boss,
· A workshop dedicated to Classification Theory for Abstract
Elementary Classes was held at the American Institute of Mathematics July 17 to
July 21 2006. More information,
· A Condensed biography of Julia Robinson,
· The
CMU pure and applied logic home page,
· American
Mathematical Society,
· Association
for Symbolic Logic,
· Mathematics web sites around the world,
· Mathematical Logic around the world,
· National Research Council's ranking of PhD programs, last time updated
1994,
· Pictures I have taken in Bogota during BMMT
2003 , can be found here.
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Personal |
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Rami@cmu.edu
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Last modified: August 25, 2024. |