$\operatorname$ is a c

01.12.2016 15:00 - 16:30

S. Uhlenbrock (U Wien)

Let \(x\) be a real of sufficiently high Turing degree, let \(\kappa_x\) be the least inaccessible cardinal in \(L[x]\) and let \(G\) be \(Col(\omega, \kappa_x)\)-generic over \(L[x]\). Then Woodin has shown that \(\operatorname\) is a core model, together with a fragment of its own iteration strategy.

Our plan is to extend this result to mice which have finitely many Woodin cardinals. We will introduce a direct limit system of mice due to Grigor Sargsyan and sketch a scenario to show the following result. Let \(n \geq 1\) and let \(x\) again be a real of sufficiently high Turing degree. Let \(\kappa_x\) be the least inaccessible strong cutpoint cardinal of \(M_n(x)\) such that \(\kappa_x\) is a limit of strong cutpoint cardinals in \(M_n(x)\) and let \(g\) be \(Col(\omega, \kappa_x)\)-generic over \(M_n(x)\). Then \(\operatorname\) is again a core model, together with a fragment of its own iteration strategy.

This is joint work with Grigor Sargsyan.

Organiser:

KGRC

Location:
SR 101, 2. St., Währinger Str. 25