| Description |
1 online resource (v, 101 pages) |
| Series |
Memoirs of the American Mathematical Society, 0065-9266 ; volume 249, number 1187 |
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Memoirs of the American Mathematical Society ; no. 1187.
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| Contents |
Introduction -- Definitions -- The Atomic Model Theorem and Related Principles -- Defining Homogeneity -- Closure Conditions and Model Existence -- Extension Functions and Model Existence -- The Reverse Mathematics of Model Existence Theorems -- Open Questions -- Appendix A: Approximating Generics -- Appendix B: Atomic Trees -- Appendix C: Saturated Models -- Bibliography |
| Summary |
Goncharov and Peretyat'kin independently gave necessary and sufficient conditions for when a set of types of a complete theory T is the type spectrum of some homogeneous model of T. Their result can be stated as a principle of second order arithmetic, which is called the Homogeneous Model Theorem (HMT), and analyzed from the points of view of computability theory and reverse mathematics. Previous computability theoretic results by Lange suggested a close connection between HMT and the Atomic Model Theorem (AMT), which states that every complete atomic theory has an atomic model. The authors sh |
| Notes |
"Volume 249, Number 1187 (eighth of 8 numbers), September 2017." |
| Bibliography |
Includes bibliographical references (pages 99-101) |
| Notes |
Print version record |
| Subject |
Reverse mathematics.
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Computable functions.
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Decidability (Mathematical logic)
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MATHEMATICS -- General.
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Computable functions
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Decidability (Mathematical logic)
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Reverse mathematics
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| Form |
Electronic book
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| Author |
Lange, Karen, 1980- author.
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Shore, Richard A., 1946- author.
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American Mathematical Society, publisher.
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| ISBN |
9781470441418 |
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1470441411 |
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