An introdution to forcing

为实现Cichoń最大值的强制技术：维也纳大学的研讨会讲义

Forcing techniques for Cichoń's Maximum: Lecture notes for the mini-course at the University of Vienna

本文探讨通过强制技术构建Cichoń最大值模型的方法，消除了对大基数的依赖，展示相关集合论特征之间的关系。

Descriptive set theory and forcing; How to prove theorems about Borel sets the hard way

These are lecture notes from a course I gave at the University of Wisconsin during the Spring semester of 1993. Part 1 is concerned with Borel hierarchies. Section 13 contains an unpublished theorem of Fremlin concerning Borel hierarchies and MA. Section 14 and 15 contain new results concerning the lengths of Borel hierarchies in the Cohen and random real model. Part 2 contains standard results on the theory of Analytic sets. Section 25 contains Harrington's Theorem that it is consistent to have $Π^1_2$ sets of arbitrary cardinality. Part 3 has the usual separation theorems. Part 4 gives some …

An introduction to forcing axioms, SRP and OCA

These notes are extracted from the lectures on forcing axioms and applications held by professor Matteo Viale at the University of Turin in the academic year 2011-2012. Our purpose is to give a brief account on forcing axioms with a special focus on some consequences of them (SRP, OCA, PID). These principles were first isolated by Todor\v cević and interpolate most consequences of MM and PFA, thus providing a useful insight on the combinatorial structure of the theory of forcing axioms. In the first part of this notes we will give a brief account on forcing axioms, introducing some equivalent …