The downward directed grounds hypothesis and very large cardinals
作者： Toshimichi Usuba
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摘要: A transitive model $M$ of ZFC is called a ground if the universe $V$ set forcing extension $M$. We show that grounds are downward set-directed. Consequently, we establish some fundamental theorems on method and set-theoretic geology. For instance, (1) mantle, intersection all grounds, must be ZFC. (2) has only many mantle ground. also very large cardinal, then
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