“Bulletin Board”

 School of Mathematics - December 26, 2004

Dissertation Defense

SH. Mohsenipour, the fifth Ph.D. student of IPM in Mathematical Logic, is going to defend his thesis entitled "Elementary End Extensions in Model Theory and Set Theory" on Monday, Jan 3, 2005. His supervisor is Prof. Ali Enayat (American University, USA).

 
 
SH. Mohsenipour, the fifth Ph.D. student of IPM in Mathematical Logic, is going to defend his thesis entitled "Elementary End Extensions in Model Theory and Set Theory" on Monday, Jan 3, 2005. His
supervisor is Prof. Ali Enayat (American University, USA).

Abstract

Our work deals with model theory of ordered structures in the domain of end ex�tension problems. We prove four new theorems in this dissertation. Theorem I generalizes a classical theorem of Keisler and Morley and positively answers a question of Enayat. Theorems II and III deal with recursively saturated models, and is inspired by the works of Shelah and Schmerl (respectively). Finally, theorem IV fine�tunes a fundamental result of Keisler on singular�like models.

  • Theorem I. Every countable model of ZFC has elementary end exten�sions with arbitrary cofinality.

  • Theorem II. Suppose κ is an inaccessible cardinal and T is a first�order theory with a κ�like model. Let A be a countable recursively saturated model of T . Then A has an elementary end extension with arbitrary cardinality and cofinality.

  • Theorem III. Suppose κ is an inaccessible cardinal and T is a first�order theory with a κ�like model that embeds a stationary subset of κ. Let A be a countable recursively saturated model of T . Then A has a blunt minimal elementary end extension.

  • Theorem IV. Suppose κ is an inaccessible cardinal and T is a first�order theory with a κ�like model. Let λ be a singular cardinal, then Keisler λ�like models of T can be represented as the union of a nice elementary end extension chain.


Information
Time: Monday, Jan 3, 2005, 17:00.
Place:School of Mathematics, Niavaran Bldg., Niavaran Square, Tehran, Iran.


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