一致地，不存在具有Sacks或Laver性质的非平凡ccc力迫概念

Selection Principles in the Laver, Miller, and Sacks models

This article is devoted to the interplay between forcing with fusion and combinatorial covering properties. We discuss known instances of this interplay as well as present a new one, namely that in the Laver model for the consistency of the Borel's conjecture, the Hurewicz property is preserved by finite products of metrizable spaces.

更有说服力的力迫概念暗示钻石

More forcing notions imply diamond

我们证明了Sacks强迫使连续统崩溃到支配数d上，回答了Carlson和Laver的问题。接下来，我们证明，如果一个适当的强制的大小在最连续的崩溃ω_2，然后它迫使diamond_{omega_1}。

Joint Laver diamonds and grounded forcing axioms

I explore two separate topics: the concept of jointness for set-theoretic guessing principles, and the notion of grounded forcing axioms. A family of guessing sequences is said to be joint if all of its members can guess any given family of targets independently and simultaneously. I primarily investigate jointness in the case of various kinds of Laver diamonds. In the case of measurable cardinals I show that, while the assertions that there are joint families of Laver diamonds of a given length get strictly stronger with increasing length, they are all equiconsistent. This is contrasted with …

Some considerations on Amoeba forcing notions

In this paper we analyse some notions of amoeba for tree forcings. In particular we introduce an amoeba-Silver and prove that it satisfies quasi pure decision but not pure decision. Further we define an amoeba-Sacks and prove that it satisfies the Laver property. We also show some application to regularity properties. We finally present a generalized version of amoeba and discuss some interesting associated questions.

漫步天堂

Strolling through Paradise

对于每一个常见的树强迫，我（例如，I = Sacks强迫S，Laver强迫L，Miller强迫M，Mathias强迫R等）我们将一个sigma理想i^0关联到实数上如下：A \in i^0当且仅当对于所有T \in I，存在S \leq T（即S比T强，或者等价地，S是T的子树）使得A \cap [S]= \emptyset，其中[S]表示通过S的分支的集合。因此，s^0是Marczewski空集的理想，r^0是Ramsey空集的理想（无处Ramsey集）等。我们证明（在ZFC中），只要i^0，j^0是两个这样的理想，则i^0 \sem j^0 \neq \emptyset。例如，在一个示例中，对于I = S和J = R，这给出了一个不是Ramsey的Marczewski零集，推广了Aniszczyk，Frankiewicz，Plewik，Brown和Corazza的部分结果，并回答了后者的一个问题.在情况下，我= M和J = L这给了米勒零集这不是紫菜零;这回答了一个问题所解决的斯皮纳斯。我们还调查的问题，这对理想被认为是正交的，哪些不是。此外，我们还讨论了Mycielski理想P_2。

一个参数化的$\diamondsuit$用于Laver性质和$\mathcal P(ω)/\mathrm{Fin}$的非平凡自同构

A parametrized $\diamondsuit$ for the Laver property and nontrivial automorphisms of $\mathcal P(ω)/\mathrm{Fin}$

本文提出参数化$\diamondsuit(\mathsf{LP})$原理，证明其在特定forcing模型中成立，并展示其导致$\mathcal P(ω)/\mathrm{Fin}$存在非平凡自同构。