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Fine Structure

In: Handbook of Set Theory

Author

Listed:
  • Ralf Schindler

    (Universität Münster, Institut für mathematische Logik und Grundlagenforschung)

  • Martin Zeman

    (University of California at Irvine, Department of Mathematics)

Abstract

The chapter on fine structure theory presents an abstract approach to fine structure theory of acceptable structures. No prerequisities are assumed except basic set-theoretic background, so the chapter may be considered an introductory text into the subject for a broad audience. Apart from this, the text is intended to be a prerequisite to Handbook chapters “Covering Lemma” by W. Mitchell and “Outline of Inner Model Theory” by J. Steel. The presentation of the material reflects this intention. The material covered in the chapter includes basic facts about acceptable structures, detailed treatment of projecta, standard codes and reducts, and extensions of embeddings theorems. At the end of the chapter two classical applications of the theory are sketched: Jensen’s construction of a square sequence in L and his proof of the Covering Lemma for L.

Suggested Citation

  • Ralf Schindler & Martin Zeman, 2010. "Fine Structure," Springer Books, in: Matthew Foreman & Akihiro Kanamori (ed.), Handbook of Set Theory, chapter 9, pages 605-656, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4020-5764-9_10
    DOI: 10.1007/978-1-4020-5764-9_10
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