Search results

Herbrand's theorem is a fundamental result of mathematical logic obtained by Jacques Herbrand (1930). It essentially allows a certain kind of reduction...

include structural proof theory, ordinal analysis, provability logic, reverse mathematics, proof mining, automated theorem proving, and proof complexity. Much...

logic dealing with proving mathematical theorems by computer programs. Automated reasoning over mathematical proof was a major impetus for the development...

constructive consistency proof for a weak system of arithmetic. The proof uses the above-mentioned, proof-theoretic Herbrand's theorem. Herbrand finished his doctorate...

methods in the theory of modular forms. A more elementary proof of Ribet's converse to Herbrand's theorem, a consequence of the theory of Euler systems...

Heijenoort's commentary and Herbrand's 1930 On the consistency of arithmetic in van Heijenoort 1967, pp. 618ff. A consistency proof often assumes the consistency...

Wiles (1990). These proofs were modeled upon Ken Ribet's proof of the converse to Herbrand's theorem (the Herbrand–Ribet theorem). Karl Rubin found a...

formulas in Σ . {\displaystyle \Sigma .} Barwise compactness theorem Herbrand's theorem – reduction of first-order mathematical logic to propositional...

Wiles (1990). These proofs were modeled upon Ken Ribet's proof of the converse to Herbrand's theorem (the so-called Herbrand–Ribet theorem). Karl Rubin found...

The Artin–Zorn theorem generalizes the theorem to alternative rings: every finite alternative division ring is a field. The original proof was given by...

sets) Helmholtz theorem (classical mechanics) (physics) Helmholtz's theorems (physics) Herbrand's theorem (logic) Herbrand–Ribet theorem (cyclotomic fields)...

number theory and algebraic geometry. He is known for the Herbrand–Ribet theorem and Ribet's theorem, which were key ingredients in the proof of Fermat's...

generalized to apply to non-prenex formulas as well, in order to prove Herbrand's theorem (Herbrand 1930). The resulting formula is not necessarily equivalent to...

Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic...

situation. In set theory, universes are often classes that contain (as elements) all sets for which one hopes to prove a particular theorem. These classes...

Verlag. Rosser, J. B. (1939). "An Informal Exposition of Proofs of Godel's Theorem and Church's Theorem". The Journal of Symbolic Logic. 4 (2): 53–60. doi:10...

The theory is developed in a uniform way, starting with topological fields, properties of Haar measure on locally compact fields, the main theorems of...

the Kronecker–Weber theorem (with a slight gap). 1896 David Hilbert gives the first complete proof of the Kronecker–Weber theorem. 1897 Weber introduces...

hierarchy theorem Space hierarchy theorem Natural proof Hypercomputation Oracle machine Rózsa Péter Alonzo Church Emil Post Alan Turing Jacques Herbrand Haskell...

Craig's interpolation theorem is a result about the relationship between different logical theories. Roughly stated, the theorem says that if a formula...