In the Shadows of the Löwenheim-Skolem Theorem: Early Combinatorial Analyses of Mathematical Proofs

DOI10.2178/bsl/1185803805zbMath1139.03004OpenAlexW2037922190MaRDI QIDQ5421030

Jan von Plato

Publication date: 22 October 2007

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

Full work available at URL: https://projecteuclid.org/euclid.bsl/1185803805

zbMATH Keywords

combinatoricslattice theoryderivabilityproof theoryprojective geometryHeyting algebraset theoryGödelSkolem

Mathematics Subject Classification ID

History of mathematics in the 20th century (01A60) Biographies, obituaries, personalia, bibliographies (01A70) History of mathematical logic and foundations (03-03) Proof theory in general (including proof-theoretic semantics) (03F03) Free lattices, projective lattices, word problems (06B25) History of combinatorics (05-03) History of ordered structures (06-03)

Related Items (5)

Gentzen's Proof Systems: Byproducts in a Work of Genius ⋮ Combinatorial analysis of proofs in projective and affine geometry ⋮ GENERALITY AND EXISTENCE: QUANTIFICATIONAL LOGIC IN HISTORICAL PERSPECTIVE ⋮ KURT GÖDEL’S FIRST STEPS IN LOGIC: FORMAL PROOFS IN ARITHMETIC AND SET THEORY THROUGH A SYSTEM OF NATURAL DEDUCTION ⋮ Constructibility and Geometry

Cites Work

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• The word and generator problems for lattices
• Natural deduction with general elimination rules
• Contraction-free sequent calculi for geometric theories with an application to Barr's theorem
• Permutability of rules in lattice theory.
• Skolem's discovery of Gödel-Dummett logic
• The axioms of constructive geometry
• Decision methods for linearly ordered Heyting algebras
• Solvable cases of the decision problem
• On closed elements in closure algebras
• Resolution and the Origins of Structural Reasoning: Early Proof-Theoretic Ideas of Hertz and Gentzen
• Proof systems for lattice theory
• Polynomial Time Uniform Word Problems
• Some theorems about the sentential calculi of Lewis and Heyting

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