Every two elementarily equivalent models have isomorphic ultrapowers

DOI10.1007/BF02771574zbMath0224.02045OpenAlexW2072087802MaRDI QIDQ2548251

Publication date: 1971

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02771574

Mathematics Subject Classification ID

Ultraproducts and related constructions (03C20)

Related Items

Elementary and algebraic properties of the Arens-Kaplansky constructions, Combinatorics with Definable Sets: Euler Characteristics and Grothendieck Rings, Isomorphic limit ultrapowers for infinitary logic, Representable posets, Cofinality spectrum theorems in model theory, set theory, and general topology, On elementary equivalence for equality-free logic, Orderable groups, elementary theory, and the Kaplansky conjecture, Ultrapowers and Local Properties of Banach Spaces, The strength of the isomorphism property, CONTINUOUS SENTENCES PRESERVED UNDER REDUCED PRODUCTS, Alfred Tarski's work in model theory, The Keisler–Shelah isomorphism theorem and the continuum hypothesis, Remarks on the diagonal embedding and strong 1-boundedness, Constructions of classical models by means of Kripke models (Survey), The Keisler-Shelah isomorphism theorem and the continuum hypothesis. II, The contributions of Alfred Tarski to general algebra, Universal algebraic methods for non-classical logics, Regular bi-interpretability of Chevalley groups over local rings, Elementary properties of free extensions, Existence of optimal ultrafilters and the fundamental complexity of simple theories, The model theory of Cohen rings, Elementary and universal equivalence of group rings, Positive logics, On Turner’s theorem and first-order theory, Lelek's problem is not a metric problem, Tilting modules arising from ring epimorphisms., Saturation and elementary equivalence of \(C^\ast\)-algebras, Vive la différence. III, Unnamed Item, One dimensional tilting modules are of finite type., Model theory of operator algebras III: elementary equivalence and II₁factors, Elementary equivalence of linear groups over rings with a finite number of central idempotents and over Boolean rings., Game sentences and ultrapowers, Horn Classes and Reduced Direct Products, Finiteness is not a \(\Sigma_0\)-property, Adequate Ultrafilters of Special Boolean Algebras, When do two Banach spaces have isometrically isomorphic nonstandard hulls, An introduction to forking, Strongly representable atom structures of relation algebras, Boolean powers, Operations on elementary classes of groups, Ultraproducts and elementary types of some groups related to infinite symmetric groups, Saturated models in institutions, A hierarchy of maps between compacta, Ultrafilters and Independent Sets, The ℵ₁-categoricity of strictly upper triangular matrix rings over algebraically closed fields, Elementary equivalence and relatively free products of lattices, Whither semantics?, On the axiomatizability of certain classes of modules, Polynomial time ultrapowers and the consistency of circuit lower bounds, Relating structure and power: comonadic semantics for computational resources (extended abstract), A semigroup of theories and its lattice of idempotent elements, Elementar äquivalente Körper und ihre absolute Galoisgruppe, Recursive axiomatizations for representable posets, Cylindric Algebras of First-Order Languages, Relating Structure and Power: Comonadic Semantics for Computational Resources, A.D. Taimanov and model theory in Kazakhstan, Key notions of Tarski's methodology of deductive systems, Isomorphisms and elementary equivalence of Chevalley groups over commutative rings, Realism and empirical equivalence, On conceptual completeness of syntactic-semantical systems, Pseudovarieties, generalized varieties and similarly described classes, RECURSIVE AXIOMATISATIONS FROM SEPARATION PROPERTIES, On some properties a projective model class passes on to the generated axiomatic class

Cites Work