Computable categoricity for algebraic fields with splitting algorithms

DOI10.1090/S0002-9947-2014-06093-5zbMath1375.03052arXiv1111.1205OpenAlexW2594570984MaRDI QIDQ5246987

Alexandra Shlapentokh, Russell G. Miller

Publication date: 22 April 2015

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1111.1205

zbMATH Keywords

splitting algorithmcomputable categoricitycomputably presented algebraic fields

Mathematics Subject Classification ID

Polynomials in general fields (irreducibility, etc.) (12E05) Computable structure theory, computable model theory (03C57) Theory of numerations, effectively presented structures (03D45) Model theory of fields (12L12) Categoricity and completeness of theories (03C35)

Related Items (15)

Degrees of autostability relative to strong constructivizations of graphs ⋮ Degrees of autostability for prime Boolean algebras ⋮ Degrees of autostability for linear orders and linearly ordered abelian groups ⋮ Effective categoricity for distributive lattices and Heyting algebras ⋮ Effective algebraicity ⋮ Classifications of computable structures ⋮ Strong degrees of categoricity and weak density ⋮ DEGREES OF CATEGORICITY AND SPECTRAL DIMENSION ⋮ A COMPUTABLE FUNCTOR FROM GRAPHS TO FIELDS ⋮ Computability-theoretic categoricity and Scott families ⋮ Degrees of categoricity of rigid structures ⋮ Categoricity spectra of computable structures ⋮ The degree of decidable categoricity of a model with infinite solutions for complete formulas ⋮ Degrees of bi-embeddable categoricity ⋮ Categoricity properties for computable algebraic fields

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