Dissertation DefenseSH. 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 extension 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 ﬁnetunes a
fundamental result of Keisler on singularlike models.

Theorem I.
Every countable model of ZFC has
elementary end extensions with arbitrary coﬁnality.

Theorem II. Suppose κ is an inaccessible
cardinal and T is a ﬁrstorder theory with a κlike 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 ﬁrstorder theory with a κlike 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 ﬁrstorder theory with a κlike model. Let λ be
a singular cardinal, then Keisler λlike 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. 
 
