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Extendibility of embeddings. (English) Zbl 0999.03046

Summary: Lifting given embeddings is an important technique in core model theory. However, the structure constructed in the lifting process (called pseudoultrapower) is not necessarily well-founded. We are going to discuss criteria for getting well-foundedness. One of them will be a generalization of the well-known Frequent Extension of Embeddings Lemma. In addition, we will show that this statement is in some sense proven optimal. This survey tries to give the idea behind this technique avoiding most details.

MSC:

03E45 Inner models, including constructibility, ordinal definability, and core models
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