Ordered Groups: A Case Study in Reverse Mathematics

DOI10.2307/421140zbMath0922.03078DBLPjournals/bsl/Solomon99OpenAlexW4244366408WikidataQ56226698 ScholiaQ56226698MaRDI QIDQ4254643

D. Reed Solomon

Publication date: 12 September 1999

Published in: Bulletin of Symbolic Logic (Search for Journal in Brave)

Full work available at URL: http://www.math.ucla.edu/~asl/bsl/0501-toc.htm

zbMATH Keywords

surveyordered groupscomputability theoryreverse mathematicsexpository paper

Mathematics Subject Classification ID

Research exposition (monographs, survey articles) pertaining to mathematical logic and foundations (03-02) Ordered groups (06F15) Second- and higher-order arithmetic and fragments (03F35) Ordered abelian groups, Riesz groups, ordered linear spaces (06F20) Theory of numerations, effectively presented structures (03D45)

Related Items (5)

Infinite dimensional proper subspaces of computable vector spaces ⋮ Structure of semisimple rings in reverse and computable mathematics ⋮ Computability-theoretic and proof-theoretic aspects of partial and linear orderings ⋮ – CA₀ and order types of countable ordered groups ⋮ The complexity of ascendant sequences in locally nilpotent groups

Cites Work

• Weak comparability of well orderings and reverse mathematics
• Countable algebra and set existence axioms
• Recursion theory and ordered groups
• Reverse mathematics and ordinal exponentiation
• Which set existence axioms are needed to prove the separable Hahn-Banach theorem?
• Algebraic disguises of \(\Sigma ^ 0_ 1\) induction
• Which set existence axioms are needed to prove the Cauchy/Peano theorem for ordinary differential equations?
• Partial realizations of Hilbert's program
• Hilbert's program relativized; Proof-theoretical and foundational reductions
• Effective content of field theory
• Class groups of integral group rings

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