Vaught's conjecture for quite o-minimal theories
نویسندگان
چکیده
منابع مشابه
Randomizing O-minimal Theories
The randomization of a complete first order theory T is the complete continuous theory T R with two sorts, a sort for random elements of models of T , and a sort for events in an underlying atomless probability space. We show that if T has the exchange property and acl = dcl, then T R has a strict independence relation in the home sort, and hence is real rosy. In particular, if T is o-minimal, ...
متن کاملTypes in o - minimal theories
Types in o-minimal theories by Janak Daniel Ramakrishnan Doctor of Philosophy in Mathematics University of California, Berkeley Professor Thomas Scanlon, Chair We extend previous work on classifying o-minimal types, and develop several applications. Marker developed a dichotomy of o-minimal types into “cuts” and “noncuts,” with a further dichotomy of cuts being either “uniquely” or “non-uniquel...
متن کاملWild theories with o-minimal open core
Let T be a consistent o-minimal theory extending the theory of densely ordered groups and let T ′ be a consistent theory. Then there is a complete theory T ∗ extending T such that T is an open core of T ∗, but every model of T ∗ interprets a model of T ′. If T ′ is NIP, T ∗ can be chosen to be NIP as well. From this we deduce the existence of an NIP expansion of the real field that has no dista...
متن کاملDefinable choice for a class of weakly o-minimal theories
Given an o-minimal structure M with a group operation, we show that for a properly convex subset U , the theory of the expanded structure M′ = (M, U) has definable Skolem functions precisely when M′ is valuational. As a corollary, we get an elementary proof that the theory of any such M′ does not satisfy definable choice. §
متن کاملThe Borel Complexity of Isomorphism for O-Minimal Theories
Given a countable o-minimal theory T , we characterize the Borel complexity of isomorphism for countable models of T up to two model-theoretic invariants. If T admits a nonsimple type, then it is shown to be Borel complete by embedding the isomorphism problem for linear orders into the isomorphism problem for models of T . This is done by constructing models with specific linear orders in the t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 2017
ISSN: 0168-0072
DOI: 10.1016/j.apal.2016.09.002