Abstract
We use a reverse Easton forcing iteration to obtain a universe with a definable well-ordering, while preserving the GCH and proper classes of a variety of very large cardinals. This is achieved by using the principle at a proper class of cardinals k. By choosing the cardinals at which coding occurs sufficiently sparsely, we are able to lift the ambeddings witnessing the large cardinal properties without having to meet any non-trivial master conditions.
| Translated title of the contribution | Large cardinals and definable well-orderings of the universe |
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| Original language | English |
| Publication status | Published - 16 Nov 2007 |