Gerhard Gentzen

German mathematician

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Gerhard Gentzen was a German logician and mathematician known for his significant contributions to proof theory. He developed the sequent calculus, a formal system for logic, which proved fundamental in understanding proof structures. Gentzen's work also extended to consistency proofs, notably for number theory, demonstrating that certain mathematical systems are free from contradictions. His research, building on the work of logicians like Gottlob Frege, advanced the formal study of logic and mathematics in the 20th century.123

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metalogic
Consistency proofs
…that of the German mathematician Gerhard Gentzen (1936) for the system N of classical (or ordinary, in contrast to intuitionistic) number theory. Taking ω (omega) to represent the next number beyond the natural numbers (called the “first transfinite number”), Gentzen’s proof employs an induction in the realm of transfinite numbers…
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…that of the German mathematician Gerhard Gentzen (1936) for the system N of classical (or ordinary, in contrast to intuitionistic) number theory. Taking ω (omega) to represent the next number beyond the natural numbers (called the “first transfinite number”), Gentzen’s proof employs an induction in the realm of transfinite numbers…
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history of logic
Syntax and proof theory
…introduced by the German logician Gerhard Gentzen (1909–45) and was initially for first-order logic. His system is known as a sequent calculus. Gentzen was able to prove in terms of sequent calculi some of the most basic results of proof theory. His first Hauptsatz (fundamental theorem) essentially showed that all…
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…introduced by the German logician Gerhard Gentzen (1909–45) and was initially for first-order logic. His system is known as a sequent calculus. Gentzen was able to prove in terms of sequent calculi some of the most basic results of proof theory. His first Hauptsatz (fundamental theorem) essentially showed that all…
Read More