The following question is open: Does there exist a hyperarithmetic class of computable structures with at least one, but only finitely many, properly \(\Sigma^1_1\) isomorphism classes? Given any oracle \(x\) in \(2^\omega\), we can ask the same question relativized to \(x\) (that is, replace hyperarithmetic, computable, and \(\Sigma^1_1\) by hyperarithmetic-in-\(x\), computable-in-\(x\), and \(\Sigma^1_1\)-in-\(x\)). A negative answer for all \(x\) implies Vaught's Conjecture for infinitary logic.
Isomorphism of Computable Structures and Vaught's Conjecture
12.01.2012 15:00 - 16:30
Organiser:
KGRC
Location:
SR 101, 2. St., Währinger Str. 25