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Induction, bounding, weak combinatorial principles, and the homogeneous model theorem / Denis R. Hirschfeldt, Karen Lange and Richard A. Shore.

By: Contributor(s): Material type: TextTextSeries: Memoirs of the American Mathematical Society ; v 249, no 1187.Publication details: Providence : American Mathematical Society, 2017.Description: v, 101 pages ; 26 cmISBN:
  • 9781470426576 (alk. paper)
Subject(s): DDC classification:
  • 510 23 Am512
Contents:
1. Introduction -- 2. Definitions -- 3. The Atomic Model Theorem and Related Principles -- 4. Defining Homogeneity -- 5. Closure Conditions and Model Existence -- 6. Extension Functions and Model Existence -- 7. The Reverse Mathematics of Model Existence Theorems -- 8. Open Questions -- Appendix A: Approximating Generics -- Appendix B: Atomic Trees -- Appendix C: Saturated Models -- Bibliography.
Summary: The authors show that HMT and AMT are indeed equivalent in the sense of reverse mathematics, as well as in a strong computability theoretic sense and do the same for an analogous result of Peretyat'kin giving necessary and sufficient conditions for when a set of types is the type spectrum of some model.
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Includes bibliographical references.

1. Introduction --
2. Definitions --
3. The Atomic Model Theorem and Related Principles --
4. Defining Homogeneity --
5. Closure Conditions and Model Existence --
6. Extension Functions and Model Existence --
7. The Reverse Mathematics of Model Existence Theorems --
8. Open Questions --
Appendix A: Approximating Generics --
Appendix B: Atomic Trees --
Appendix C: Saturated Models --
Bibliography.

The authors show that HMT and AMT are indeed equivalent in the sense of reverse mathematics, as well as in a strong computability theoretic sense and do the same for an analogous result of Peretyat'kin giving necessary and sufficient conditions for when a set of types is the type spectrum of some model.

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