Rami Grossberg
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Rami Grossberg | |
---|---|
רמי גרוסברג | |
Occupation | Professor |
Spouse | University of Jerusalem Ph.D. (1986) |
Academic work | |
Discipline | Mathematics |
Sub-discipline | Model theory |
Institutions | Carnegie Mellon University |
Doctoral students | Monica VanDieren |
Rami Grossberg (Hebrew: רמי גרוסברג) is a full professor of mathematics at Carnegie Mellon University and works in model theory.
Work
Grossberg's work in the past few years has revolved around the
Some of Grossberg's work may be understood as part of the big project on Saharon Shelah's outstanding categoricity conjectures:
Conjecture 1. (Categoricity for ). Let be a sentence. If is categorical in a cardinal then is categorical in all cardinals . See Infinitary logic and Beth number.
Conjecture 2. (Categoricity for AECs) See [1] and [2]. Let K be an AEC. There exists a cardinal μ(K) such that categoricity in a cardinal greater than μ(K) implies categoricity in all cardinals greater than μ(K). Furthermore, μ(K) is the Hanf number of K.
Other examples of his results in pure model theory include: generalizing the Keisler–Shelah omitting types theorem for to successors of singular cardinals; with Shelah, introducing the notion of unsuper-stability for infinitary logics, and proving a nonstructure theorem, which is used to resolve a problem of Fuchs and Salce in the theory of modules; with Hart, proving a structure theorem for , which resolves Morley's conjecture for excellent classes; and the notion of relative saturation and its connection to Shelah's conjecture for .
Examples of his results in applications to algebra include the finding that under the weak continuum hypothesis there is no universal object in the class of uncountable locally finite groups (answering a question of Macintyre and Shelah); with Shelah, showing that there is a jump in cardinality of the abelian group Extp(G, Z) at the first singular strong limit cardinal.
Personal life
In 1986, Grossberg attained his doctorate from the
References
- ^ "Rami Grossberg - The Mathematics Genealogy Project". www.genealogy.math.ndsu.nodak.edu. Retrieved 2023-09-27.
- ^ Roth, Mark (June 1, 2009), "The Thinkers: RMU professor finds beauty in math", Pittsburgh Post-Gazette
External links
- Rami Grossberg
- Rami Grossberg at the Mathematics Genealogy Project
- Rami Grossberg publications indexed by Google Scholar
- A survey of recent work on AECs