Trivial, strongly minimal theories are model complete after naming constants
نویسندگان
چکیده
منابع مشابه
Trivial, Strongly Minimal Theories Are Model Complete after Naming Constants
We prove that ifM is any model of a trivial, strongly minimal theory, then the elementary diagram Th(MM ) is a model complete LM -theory. We conclude that all countable models of a trivial, strongly minimal theory with at least one computable model are 0′′-decidable, and that the spectrum of computable models of any trivial, strongly minimal theory is Σ5. The purely model-theoretic result in th...
متن کاملStrongly Minimal Theories with Recursive Models
We give effectiveness conditions on a strongly minimal theory T guaranteeing that all models have computable copies. In particular, we show that if T is strongly minimal and for n ě 1, T X Dn`2 is ∆n, uniformly in n, then every model has a computable copy. Relativizing, we answer a long-standing question in computable model theory, showing that if a strongly minimal theory has a computable mode...
متن کاملOn the Computability-theoretic Complexity of Trivial, Strongly Minimal Models
We show the existence of a trivial, strongly minimal (and thus uncountably categorical) theory for which the prime model is computable and each of the other countable models computes 0′′. This result shows that the result of Goncharov/Harizanov/Laskowski/Lempp/McCoy (2003) is best possible for trivial strongly minimal theories in terms of computable model theory. We conclude with some remarks a...
متن کاملStrongly n-trivial Knots
We prove that given any knot k of genus g, k fails to be strongly n-trivial for all n, n ≥ 3g − 1.
متن کاملThe elementary diagram of a trivial, weakly minimal structure is near model complete
We prove that if M is any model of a trivial, weakly minimal theory, then the elementary diagram T (M) eliminates quantifiers down to Boolean combinations of certain existential formulas.
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: Proceedings of the American Mathematical Society
سال: 2003
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-03-06951-x