Supercompact Extender Based Magidor-Radin Forcing

Intermediate Models of Magidor-Radin Forcing- Part II

We continue the work done by the authors and before that by the second author, Kanovei and koepke. We prove that for every set of ordinals $A$ in a Magidor-Radin generic extension using a coherent sequence such that $o^{\vec{U}}(κ)<κ^+$, there is $C'\subseteq C_G$, such that $V[A]=V[C']$. Also we prove that the supremum of a fresh set in a Prikry, tree Prikry, Magidor, Radin-Magidor and Radin forcing, changes cofinality to $ω$.

Intermediate Models in Magidor-Radin Forcing- Part I

We continue the work done by Gitik, Kanovei, Koepke, and later by the authors. We prove that for every set $A$ in a Magidor-Radin generic extension using a coherent sequence such that $o^{\vec{U}}(κ)<κ$, there is a subset $C'$ of the Magidor club such that $V[A]=V[C']$. Also we classify all intermediate $ZFC$ transitive models $V\subseteq M\subseteq V[G]$.

无顶端扩展子的基于扩展子的Magidor-Radin迫迫

Extender-based Magidor-Radin forcings without top extenders

本文发展了无顶端扩展子的基于扩展子的Magidor-Radin迫迫，用于在不可达基数的club子集上实现SCH失败，并构造基数算术行为在stationary类上不同的模型。

Extender Based Radin Forcing

We define extender sequences, generelizing measure sequences from Radin Forcing. Using the extender sequences we combine Gitik-Magidor forcing for adding many Prikry sequences with Radin forcing. This forcing satisfies Prikry like condition, destroys no cardinals, and has a kind of properness. Depending on the large cardinal we start with, this forcing can blow the power of a cardinal together with changing its' cofinality to a prescribe value. If this prescribed value is the cardinal itself then it remains regular and even can remain measurable.

非正规 Magidor-Radin 型力迫

Non-Normal Magidor-Radin Types of Forcings

本文发展 Magidor 和 Radin 力迫的非正规变体，证明其可添加 Cohen 泛型函数，但仅在非改变共尾性情形；并证明扩展器基力迫不添加新子集，且 Gitik 力迫变体可改变可测基数共尾性至 ω₁ 并引入 Cohen 子集。

A Power Function with A Fixed Finite Gap Everywhere

We give an application of our extender based Radin forcing to cardinal arithmetic. Using a preparation forcing and interleaving of Cohen and Levy forcings in the normal Radin sequence we get a model with a power function having a fixed finite gap on all cardinals.