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Ideals and Generic Elementary Embeddings

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Handbook of Set Theory

Abstract

This chapter covers the technique of generic elementary embeddings. These embeddings are closely analogous to conventional large cardinal embeddings, the difference being that they are definable in forcing extensions of V rather than in V itself. The advantage of allowing the embeddings to be generic is that the critical points of the embeddings can be quite small, even as small as ω 1. For this reason they have many consequences for accessible cardinals, settling many classical questions of set theory.

The writing of this chapter was partially supported by grant MS-0701030 from the National Science Foundation.

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  1. Department of Mathematics, University of California at Irvine, Irvine, CA, 92697, USA

    Matthew Foreman

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  1. School of Physical Sciences, University of California, Irvine, Irvine, 92697-3875, U.S.A.

    Matthew Foreman

  2. Dept. Manufacturing Engineering, Boston University, St. Mary's St. 15, Boston, 02215, U.S.A.

    Akihiro Kanamori

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Foreman, M. (2010). Ideals and Generic Elementary Embeddings. In: Foreman, M., Kanamori, A. (eds) Handbook of Set Theory. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-5764-9_14

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