Rutgers Logic Seminars
Room 705, Hill Center
Rutgers Logic Seminar
Monday Sept 12th, 5:00-6:20 pm
Saharon Shelah, Hebrew University/Rutgers
Can we understand countable theories with few models
in $aleph_1$ (without weak CH)? A progress report.
Assume $T$ is a first order countable complete theory, which has uncountable atomic models and has few or even just one atomic model of cardinality $aleph_1$. (We can arrive to this starting from such infinitary sentence). We hope to prove that this holds absolutely and there are atomic models of cardinality continuum. Toward this we try to analyze the class $K_T$ of atomic models of $T$ and make some advances.