无选择链条件
Choiceless Chain Conditions
摘要:
链条件是强迫理论中使用的主要工具之一。我们说偏序有可数链条件,如果每个反链(在强迫的意义下)是可数的。由于各种原因,如果没有选择选择公理,反链往往用处不大,在这篇短文中,我们研究了ZFC中等价于可数链条件的一些条件。
英文摘要:
Chain conditions are one of the major tools used in the theory of forcing. We say that a partial order has the countable chain condition if every antichain (in the sense of forcing) is countable. Without the axiom of choice antichains tend to be of little use, for various reasons, and in this short note we study a number of conditions which in ZFC are equivalent to the countable chain condition.
机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。