On the Decidability and Quantifier Elimination of Transfinite Real Closed Spectra via Cylindrical Homological Decompositions
Year: 2025
Type: article
Abstract: Mathematical Applications of Science Fiction We present a hyper-canonical derivation of the decidabil-ity of the theory of Real Closed Fields (TRCF), extendingthe classical Tarskian paradigm through a rigorous topo-logical stratification of Rn. By constructing a recursiveCylindrical Algebraic Decomposition (CAD) adapted to anarbitrary finite set of polynomials P ⊂ Z[x1, . . . , xn], wedemonstrate that every formula ϕ in the language of orderedrings Lor is effectively equivalent to a quantifier-free formulaψ. We establish the existence of delineable sections oversemi-algebraic cells, proving the invariance of sign sequencesacross connected components of the decomposition. Thismanuscript provides a self-contained, transfinite proof ofthe effective elimination of quantifiers, thereby resolvingthe decision problem for TRCF with absolute algorithmicdeterminism.
Authors: MFC, 10, Revista, Zen
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7117869740
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