Rami Grossberg

Department of Mathematical Sciences
Carnegie Mellon University

Ph.D. Hebrew University of Jerusalem, 1986 (advisor: Saharon Shelah )

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My old and outdated "official" page in our departmental catalog is here.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.

Papers and theses written by PhD students while working under my guidance 

Current PhD students:

• Wentao Yang . 

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 , 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 , 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.

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. 

• This semester Will Boney is teaching in Harvard a course titeled Classification Theory for Tame Abstract Elementary Classes .  
• An article explaining that Logic is responsible to the creation of industries worth Trillions of dollars. , 
• 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, 
• The CMU math dept, 
• American Mathematical Society, 
• Association for Symbolic Logic, 
• Mathematics web sites around the world, 
• Mathematical Logic around the world, 
• MSRI lectures on video, 
• Saharon Shelah's papers. 
• 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. 

• Address and office hours, 
• Directions to my house, 
• Academic Ancestors, 
• Some pictures. 

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Rami@cmu.edu