Mathias-Prikry和Laver型强迫;可和理想、余理想和$+$ -选择滤子
Mathias--Prikry and Laver type forcing; Summable ideals, coideals, and $+$-selective filters
摘要：
我们研究了Mathias-Prikry和Laver型强迫与过滤器和余理想。我们隔离了Mathias实数的一个重要的组合性质，并证明了Mathias-Prikry强迫与可和理想都是相互双嵌入的。我们表明，马蒂亚斯强迫与一个分析理想的补充总是增加了一个占主导地位的真正的。我们还描述了过滤器的相关Mathias-Prikry强迫不添加最终不同的reals，并表明，他们是可数生成的，提供他们是博雷尔。我们给出了$ω$ -击中和$ω$ -分裂族的一个特征，这些族在与共理想相关联的Laver型强迫的扩张中保持了它们的性质。
英文摘要：
We study the Mathias--Prikry and the Laver type forcings associated with filters and coideals. We isolate a crucial combinatorial property of Mathias reals, and prove that Mathias--Prikry forcings with summable ideals are all mutually bi-embeddable. We show that Mathias forcing associated with the complement of an analytic ideal always adds a dominating real. We also characterize filters for which the associated Mathias--Prikry forcing does not add eventually different reals, and show that they are countably generated provided they are Borel. We give a characterization of $ω$-hitting and $ω$-splitting families which retain their property in the extension by a Laver type forcing associated with a coideal.
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