Department of

Mathematics


Seminar Calendar
for events the day of Tuesday, May 15, 2018.

     .
events for the
events containing  

(Requires a password.)
More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
      April 2018              May 2018              June 2018      
 Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
  1  2  3  4  5  6  7          1  2  3  4  5                   1  2
  8  9 10 11 12 13 14    6  7  8  9 10 11 12    3  4  5  6  7  8  9
 15 16 17 18 19 20 21   13 14 15 16 17 18 19   10 11 12 13 14 15 16
 22 23 24 25 26 27 28   20 21 22 23 24 25 26   17 18 19 20 21 22 23
 29 30                  27 28 29 30 31         24 25 26 27 28 29 30
                                                                   

Tuesday, May 15, 2018

1:00 pm in 345 Altgeld Hall,Tuesday, May 15, 2018

Interpolative fusions - preservation results

Alex Kruckman (IU Bloomington)

Abstract: Fix languages $L_1$ and $L_2$ with intersection $L_\cap$ and union $L_\cup$. An $L_\cup$ structure $M$ is interpolative if whenever $X_1$ is an $L_1$-definable set and $X_2$ is an $L_2$-definable set, $X_1$ and $X_2$ intersect in $M$ unless they are separated by an $L_\cap$-definable set. Examples of interpolative structures abound in model theory, but only recently did Minh Tran and Erik Walsberg begin studying the class in the abstract. When $T_1$ is an $L_1$ theory and $T_2$ is an $L_2$ theory, we are interested in the class of interpolative fusions: interpolative structures which are models of the union theory $T_\cup$. Putting aside the nontrivial question of whether this class is elementary (I will assume that it is, axiomatized by a theory $T^{*}$), I will explain how stability-theoretic assumptions on the base $L_\cap$-theory $T_\cap$ lead to preservation results of the form "If $T_1$ and $T_2$ both satisfy property $P$, then $T^{*}$ satisfies property $P$". This is joint work with Minh and Erik.