|Thursday 24 September 2020|
|Events for day: Wednesday 16 September 2020|
| 15:30 - 17:30 Mathtematical Logic Weekly Seminar|
Tameness for Set Theory
We show that (assuming large cardinals) set theory is a tractable (and we dare to say tame) first order theory when formalized in a first order signature with natural predicate symbols for the basic definable concepts of second and third order arithmetic, and appealing to the model-theoretic notions of model completeness and model companionship. Specifically we develop a general framework linking generic absoluteness results to model companionship and show that (with the required care in details) a $Pi_2$-property formalized in an appropriate language for second or third order number theory is forcible from some T extending ZFC + large car ...