实值可测性模型

一致开折与解析可测性

Uniform Unfolding and Analytic Measurability

我们考虑了P加实数的力迫概念和P-可测集的代数。对于Cohen-和Random-Forcing，我们可以使用无限对策的Solovay展开技巧证明每个解析集都是P-可测的。为了表明这一点，我们发展的概念，战略融合，并给出了一个统一的展开定理，使我们能够减少证明的分析可测性的定义，一个特定的功能证明。

阿米巴-绝对性与射影可测性

Amoeba-absoluteness and projective measurability

本文研究了Amoeba强迫（一般地在随机实数集上加一个测度的偏序）与射影可测性之间的关系。给定一个集合论的论域V和V中的一个力迫概念P，我们说V是Sigma ^1_n-P-绝对的当且仅当对于V中的每一个参数为Sigma^1_n-句子φ，我们有V模型φ当且仅当V^P模型φ。我们证明了Sigma^1_4-变形虫绝对性意味着对于所有ω中的α ^ω（ω_1 ^{L[a]} <ω_1^V），因此也意味着Sigma^1_3-可测性。这回答了Haim Judah的一个问题（私人通信）。

On the sepration of regularity properties of the reals

We present a model where ω_1 is inaccessible by reals, Silver measurability holds for all sets but Miller and Lebesgue measurability fail for some sets. This contributes to a line of research started by Shelah in the 1980s and more recently continued by Schrittesser and Friedman, regarding the separation of different notions of regularity properties of the real line.

Lowness for Integer-Valued Randomness

A real is called integer-valued random if no integer-valued martingale can win arbitrarily much capital betting against it. A real is low for integer-valued randomness if no integer-valued martingale recursive in A can succeed on an integer-valued random real. We show that lowness for integer-valued randomness coincides with recursiveness, as is the case for computable randomness.

再论实值可测基数和理想强迫

More on real-valued measurable cardinals and forcing with ideals

对D. Fremlin [实值可测基数，在实数的集合论中，H. Judah ed. 1993，151-305 ]我们证明了：（1）如果c是实值可测的，那么（c，P（c），sigma）的Maharam型是2 ^c。(2)有k个实值可测是相容的，但对于每个有k个实值可测的子模型V_1，不存在在V_1上随机的k个实值。

Residue field domination in real closed valued fields

We define a notion of residue field domination for valued fields which generalizes stable domination in algebraically closed valued fields. We prove that a real closed valued field is dominated by the sorts internal to the residue field, over the value group, both in the pure field sort and in the geometric sorts. These results characterize forking and þ-forking in real closed valued fields (and also algebraically closed valued fields). We lay some groundwork for extending these results to a power-bounded $T$-convex theory.