Model-completeness and elimination of quantifiers for subdirect products of structures

DOI10.1016/0021-8693(75)90101-5zbMath0318.02052OpenAlexW2055120326MaRDI QIDQ1222162

Volker Weispfenning

Publication date: 1975

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-8693(75)90101-5

Mathematics Subject Classification ID

Model-theoretic algebra (03C60) Connections between field theory and logic (12L99) Applications of logic to commutative algebra (13L05) Differential algebra (12H05) Ordered groups (06F15) Other classical first-order model theory (03C68)

Related Items (17)

Regular separably closed rings ⋮ Commutative regular rings and Boolean-valued fields ⋮ Hyper-regular lattice-ordered groups ⋮ Model companion and model completion of theories of rings ⋮ A valuation ring analogue of von Neumann regularity ⋮ Sheaf Constructions and Their Elementary Properties ⋮ On Boolean algebras and integrally closed commutative regular rings ⋮ Sheaves of structures, Heyting‐valued structures, and a generalization of Łoś's theorem ⋮ Sheaves and prime model extensions ⋮ Elementary equivalence of some rings of definable functions ⋮ Model theory of Boolean products of subdirectly irreducible heyting algebras ⋮ Amalgamation bases for commutative rings without nilpotent elements ⋮ Boolean products of real closed valuation rings and fields ⋮ Preservation theorems for limits of structures and global sections of sheaves of structures ⋮ A characterization of companionable, universal theories ⋮ Commutative Regular Rings with Integral Closure ⋮ The model-theoretic structure of Abelian group rings

Cites Work

• The representation of biregular rings by sheaves
• Introduction to model theory and to the metamathematics of algebra
• Model-completeness for sheaves of structures
• Hereditary Commutative Rings and Centres of Hereditary Rings
• Model-completions and modules
• The Model Companion of the Theory of Commutative Rings Without Nilpotent Elements
• Some theorems about the sentential calculi of Lewis and Heyting
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