On generlized Ehrenfeucht-Mostowski models

Seminar
Speaker
Ido Feldman (BIU)
Date
03/08/2023 - 16:00 - 14:00Add to Calendar 2023-08-03 14:00:00 2023-08-03 16:00:00 On generlized Ehrenfeucht-Mostowski models One of the main question in generalized descriptive set theory is whether there is generalized Borel-reducibility counterpart of Shelah's main gap theorem. Which is stated as follows: Let $T_1$ be a classifiable theory and $T_2$ a non-classifiable theory. Is there a Borel reduction from the isomorphism relation of $T_1$ to the isomorphism relation of $T_2$? This question was studied by Friedman, Hyttinen, and Weinstein (former Kulikov), who gave a positive answer to this question for the case $\kappa$ a successor cardinal (under certain cardinal assumptions), and $T_2$ a stable unsuperstable theory. All of the above assume the existence of diamond on a stationary set in order to execute the proof. The case when $\kappa$ is strongly-inaccessible cardinal was study by Hyttinen and Moreno. In a joint paper with Moreno, a positive answer to this question is given for $\kappa$ an inaccessible cardinal, $T_2$ a stable theory with OCP. In this talk we give a brief overview of the subject and present new result which extends to unsuperstable theories for strongly inaccessible cardinal. Thus, in particular giving a positive answer to the question without the use of diamond. Seminar room אוניברסיטת בר-אילן - המחלקה למתמטיקה mathoffice@math.biu.ac.il Asia/Jerusalem public
Place
Seminar room
Abstract

One of the main question in generalized descriptive set theory is whether there is generalized Borel-reducibility counterpart of Shelah's main gap theorem.
Which is stated as follows:
Let $T_1$ be a classifiable theory and $T_2$ a non-classifiable theory. Is there a Borel reduction from the isomorphism relation of $T_1$ to the isomorphism relation of $T_2$?

This question was studied by Friedman, Hyttinen, and Weinstein (former Kulikov), who gave a positive answer to this question for the case $\kappa$ a successor cardinal (under certain cardinal assumptions), and $T_2$ a stable unsuperstable theory.
All of the above assume the existence of diamond on a stationary set in order to execute the proof.
The case when $\kappa$ is strongly-inaccessible cardinal was study by Hyttinen and Moreno.

In a joint paper with Moreno, a positive answer to this question is given for $\kappa$ an inaccessible cardinal, $T_2$ a stable theory with OCP.

In this talk we give a brief overview of the subject and present new result which extends to unsuperstable theories for strongly inaccessible cardinal.
Thus, in particular giving a positive answer to the question without the use of diamond.

תאריך עדכון אחרון : 03/08/2023