# Rami Grossberg

### Email

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My old and outdated "official" page in our departmental catalog is here.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

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.

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

 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, 21 pages, last revision 5/15/97. ps , dvi , pdf .

18. 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 .

19. 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 .

20. 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 .

21. 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 .

22. 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 .

23. 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 .

24. Rami Grossberg and Olivier Lessmann. Abstract decomposition theorem and applications, Contemporary Mathematics, Vol 380, (2005), AMS, pp. 73--108. ps , pdf .

25. 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 .

26. 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 .

27. 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 .

28. Rami Grossberg and Alexei Kolesnikov. Superior Abstract Elementary Classes are Tame. 26 pages, last updated 9/9/05. ps , pdf . submitted.

29. 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.

30. Will Boney and Rami Grossberg. Forking in Short and Tame AECs. pdf . Ann. Pure Appl. Logic 168 (2017), no. 8, 1517--1551.

31. 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.

32. 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

33. 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 .

34. 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

I am working on three volume model theory book series:
• A course in Model Theory I: Introduction, 785 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.
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.

 Teaching
 Past Teaching Fall, 2015 Spring, 2016 Fall, 2016 Spring, 2017 Fall, 2017 Spring, 2018 Fall, 2018

 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. The seminar meets on Mondays 5-6:30PM in WeH 7201. Information about current talks and talks given the last three years can be found here.

 Personal

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 Email

Rami@cmu.edu