#  Harvard Logic Colloquium: Joel Hamkins 

 



####  calendar\_today Date and Time 

 **October 20, 2016** 

 04:00PM - 05:00PM EDT 

####  pin\_drop Location 

 **Logic Center, Room 420, 2 Arrow Street**  



 

 



 

**Joel Hamkins** (City University of New York): *Recent Advances in Set-theoretic Geology*

Set-theoretic geology is the study of the set-theoretic universe V in the context of all its ground models and those of its forcing extensions. For example, a bedrock of the universe is a minimal ground model of it and the mantle is the intersection of all grounds. In this talk, I shall explain some recent advances, including especially the breakthrough result of Toshimichi Usuba, who proved the strong downward directed grounds hypothesis: for any set-indexed family of grounds, there is a deeper common ground below them all. This settles a large number of formerly open questions in set-theoretic geology, while also leading to new questions. It follows, for example, that the mantle is a model of and provably the largest forcing-invariant definable class. Strong downward directedness has also led to an unexpected connection between large cardinals and forcing: if there is a hyper-huge cardinal k, then the universe indeed has a bedrock and all grounds use only k-small forcing.



 

 



 

 See also:- [ Harvard Logic Colloquium ](/department-events/harvard-logic-colloquium)
 
 

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