Mutually generic classes and incompatible expansions
نویسندگان
چکیده
منابع مشابه
Pairwise Incompatible Generic Families
Let M be a countable model of ZF~ . There exists a family & of 2 models of ZF each obtained from M by adjoining an A/-generic family of 2W Cohen reals, such that no two distinct models in !F have a common extension to a model of ZF~ with the same ordinals.
متن کاملMutually algebraic structures and expansions by predicates
We introduce the notion of a mutually algebraic structure and prove many equivalents. A structure M is mutually algebraic if and only if it has a weakly minimal, trivial theory if and only if every expansion (M,A) by a unary predicate does not have the finite cover property. We show that every structure has a maximal mutually algebraic reduct, and give a strong structure theorem for the class o...
متن کاملOn some classes of expansions of ideals in $MV$-algebras
In this paper, we introduce the notions of expansion of ideals in $MV$-algebras, $ (tau,sigma)- $primary, $ (tau,sigma)$-obstinate and $ (tau,sigma)$-Boolean in $ MV- $algebras. We investigate the relations of them. For example, we show that every $ (tau,sigma)$-obstinate ideal of an $ MV-$ algebra is $ (tau,sigma)$-primary and $ (tau,sigma)$-Boolean. In particular, we define an expansion $ ...
متن کاملA Non-Generic Real Incompatible with 0#
Theorem 1. Let L be a minimal countable standard transitive model of ZFC + V =L. There exists a real x ng having the following three properties: (1) x ng / ∈ L. (2) L[x ng ] satisfies ZFC. (3) In the following sense, x ng is not generic over any outer model of L: Assume that V is transitive and contains the same ordinals as L, and that P is a V-amenable partial ordering. Let 0 be the forcing re...
متن کاملGeneric Expansions of Ordered Structures
Let T be a complete first order theory in a language L satisfying uniform finiteness and let TP be the model companion of T in an expanded language LP with a new unary predicate P . We show that: TP satisfies uniform finiteness; if T is an expansion of the theory of dense linear order then every cut definable in a model M of TP is definable in M L; and, if T is an expansion of the theory dense ...
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: Fundamenta Mathematicae
سال: 1984
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm-121-3-213-218