Purchase Solution

Gerhard Gentzen

Not what you're looking for?

Ask Custom Question

What are Gerhard Gentzen's mathematical accomplishments?

Purchase this Solution

Solution Summary

This describes Gerhard Gentzen's accomplishments.

Solution Preview

At age 22 in 1932, Gentzen submitted paper #1: "On the Existence of Independent Axiom Systems for Infinite Sentence Systems." He introduces a system of the propositional calculus as a sequent calculus based on Hertz's work. He modifies Hertz's "syllogism" rule to be Gentzen's "cut" rule. In this context he constructs an infinite set of sentences that has no independent set of axioms. He also shows that all "linear" sentence systems do have an independent axiomatization.
Gentzen classifies mathematics into three levels (a classification which goes back to Weyl [1931]) based on how infinity is used: elementary number theory, analysis and general set theory. ...

Purchase this Solution


Free BrainMass Quizzes
Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts