Abstract: We combine a technique of Steel with one due to Jensen and Steel to

obtain a core model below singular cardinals kappa which are

sufficiently closed under the beth function, assuming that there is no

premouse of height kappa with unboundedly many Woodin cardinals.

The motivation for isolating such core model is computing a lower bound for the strength of

the theory: T = ''ZFC + there is a singular cardinal kappa such that the set of ordinals below kappa where GCH holds is stationary and co-stationary''.

We can apply to the above core model a technique of Gitik, Schindler and Shelah that was used to obtain a lower bound for the strength of T.

obtain a core model below singular cardinals kappa which are

sufficiently closed under the beth function, assuming that there is no

premouse of height kappa with unboundedly many Woodin cardinals.

The motivation for isolating such core model is computing a lower bound for the strength of

the theory: T = ''ZFC + there is a singular cardinal kappa such that the set of ordinals below kappa where GCH holds is stationary and co-stationary''.

We can apply to the above core model a technique of Gitik, Schindler and Shelah that was used to obtain a lower bound for the strength of T.

## Date:

Wed, 15/05/2019 - 14:00 to 15:30

## Location:

Ross 63