科研之友
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摘要
Jech proved that every partially ordered set can be embedded into the cardinals of some model of ZF. We extend this result to show that every partially ordered set can be embedded into the cardinals of some model of ZF + DC<kappa for any regular kappa. We use this theorem to show that for all kappa, the assumption of DC, does not entail that there are no decreasing chains of cardinals. We also show how to extend the result to and embed into the cardinals a proper class which is definable over the ground model. We use this extension to give a large-cardinals-free proof of independence Of the weak choice principle known as WISC from DC kappa
- 出版日期2014
