TY  - BOOK
AU  - Hirschfeldt,Denis R.
AU  - Lange,Karen
AU  - Shore,Richard A.
TI  - Induction, bounding, weak combinatorial principles, and the homogeneous model theorem
T2  - Memoirs of the American Mathematical Society
SN  - 9781470426576 (alk. paper)
U1  - 510 23
PY  - 2017///
CY  - Providence : 
PB  - American Mathematical Society, 
KW  - Reverse mathematics
KW  - Computable functions
KW  - Decidability (Mathematical logic)
N1  - 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.
N2  - 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
ER  -