Sentence examples for Large cardinal from inspiring English sources

Under suitable large cardinal axioms, the converse also holds.

By and large, Cardinal Law seems to have succeeded.

Otherwise the large cardinal is large.

Under large cardinal assumptions one has more generic extensions.

Another important, and much stronger large cardinal notion is supercompactness.

Second, V = LΩ is compatible with all large cardinal axioms.

Thus, the original large cardinal axioms imply that ΘL ≤ ℵ2.

The second approach was to invoke large cardinal axioms.

Summary: Large cardinal axioms are sufficient to prove definable determinacy and inner models of large cardinal axioms are necessary to prove definable determinacy.

The critical point is (typically) the large cardinal associated with the embedding.

Gödel's program for large cardinal axioms proved to be remarkably successful.