Induction, Bounding, Weak Combinatorial Principles, and the Homogeneous Model Theorem

Download or read book Induction, Bounding, Weak Combinatorial Principles, and the Homogeneous Model Theorem written by Denis Roman Hirschfeldt and published by . This book was released on 2017 with total page 101 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.