Non Cohen Oracle c.c.c

Oracle-树强制与十三元素情形下的Wilfs不等式

Oracle-Tree Forcing and Wilfs Inequality for Thirteen Left Elements

本文研究filter-Laver强制及其商与基数性质，证明网格贫乏理想覆盖数与贫乏理想一致，并应用该框架给出十三元素数值半群的Wilfs不等式c≤13e的完整算术证明。

Small forcings and Cohen reals

We prove it consistent relative to ZFC that all nontrivial forcings of size $\aleph _1$ add a Cohen real.

How special are Cohen and random forcings i.e. Boolean algebras of the family of subsets of reals modulo meagre or null

The feeling that those two forcing notions-Cohen and Random-(equivalently the corresponding Boolean algebras Borel(R)/(meager sets), Borel(R)/(null sets)) are special, was probably old and widespread. A reasonable interpretation is to show them unique, or ``minimal'' or at least characteristic in a family of ``nice forcing'' like Borel. We shall interpret ``nice'' as Souslin as suggested by Judah Shelah [JdSh 292]. We divide the family of Souslin forcing to two, and expect that: among the first part, i.e. those adding some non-dominated real, Cohen is minimal (=is below every one), while among…