Iterations of V and the core model

The core model for almost linear iterations

We introduce 0^h (0^handgrenade) as a sharp for an inner model with a proper class of strong cardinals. If 0^h does not exist then any normal iteration tree is "almost linear." We exploit this fact to prove the existence of the core model K in the theory "ZFC + 0^h does not exist." (As of today, non-0^h is thereby the weakest anti large cardinal assumption under which K can be shown to exist in ZFC. In this sense we improve earlier work of Dodd, Jensen, Mitchell, and - partially - Steel.) We indicate that our paper provides the last step for determining the exact consistency strength of a stat…

自然性与可定义性 III

Naturality and Definability III

本文探究范畴论自然性与模型论可定义性的关联，证明温和条件下自然性蕴含可定义性，构造出满足可一致化构造均为弱自然的ZFC传递模型，还证明公式表示的自然构造可无额外参数一致可定义，回答了Hodges与Shelah的相关问题。

More on mutual stationarity

Extending a result of Foreman and Magidor we prove that in the core model for almost linear iterations the following holds. There is a sequence (S^n_α: n<ω,α>0) such that each individual S^n_αis a stationary subset of \aleph_{α+1} consisting of points of cofinality ω_1, and for all limits λand for all f:λ-> ωdo we have that (S^{f(α)}_α: α<λ) is mutually stationary if and only if the range of f is finite.