Real closed rings, I. Residue rings of rings of continuous functions

DOI10.4064/fm-126-2-147-183zbMath0605.54014OpenAlexW974217490MaRDI QIDQ3742314

Gregory L. Cherlin, Max A. Dickmann

Publication date: 1986

Published in: Fundamenta Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/211595

zbMATH Keywords

ZFCmaximal idealMartin's axiomF-spacering of continuous functionsmeasure ultrafiltersnonisolated \(G_{\delta }\)- and \(\beta \) F-pointone- point compactifications of the countable and uncountable discrete spacespreservation under extensionprime z- idealreal closed idealsz-ultrafilters

Mathematics Subject Classification ID

Extensions of spaces (compactifications, supercompactifications, completions, etc.) (54D35) Algebraic properties of function spaces in general topology (54C40) Consistency and independence results in general topology (54A35) Topology of special sets defined by functions (54C50) Rings and algebras of continuous, differentiable or analytic functions (46E25)

Related Items (17)

Pseudo-valuation rings and \(C(X)\) ⋮ Rings and sheaves ⋮ On the Krull dimension of rings of continuous semialgebraic functions ⋮ Unnamed Item ⋮ On the spectra of rings of semialgebraic functions ⋮ SV and related \(f\)-rings and spaces ⋮ SV-rings and SV-porings ⋮ The global dimension of anf-ring via its space of minimal prime ideals ⋮ Concerning real-closed ideals in \(\mathcal{R} L\) and SV-frames ⋮ From Freudenthal's spectral theorem to projectable hulls of unital Archimedean lattice-groups, through compactifications of minimal spectra ⋮ Definable choice for a class of weakly o-minimal theories ⋮ Almost discrete SV-space ⋮ When is \(C(X)/P\) a valuation ring for every prime ideal \(P\)? ⋮ Lattice-Ordered Algebras that are Subdirect Products of Valuation Domains ⋮ A purely algebraic characterization of the hyperreal numbers ⋮ Boolean products of real closed valuation rings and fields ⋮ On the size of the fibers of spectral maps induced by semialgebraic embeddings

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