Gentzen

Gentzen noticed that in normal derivations, this property of single steps is inherited by the whole derivation, in the sense that all formulas are subformulas of the conclusion.

Chores 2009

Gentzen formulated the latter, denoted LK, so that it gave an intuitionistic calculus, denoted LJ, as a special case, the one in which the conclusion is a list of at most one case.

Chores 2009

The connection seems to have been established by Ketonen's philosophy professor Eino Kaila who had met Gentzen in 1936 in Münster.

Chores 2009

At the time when Gentzen worked out his system of natural deduction,

Chores 2009

For Gentzen, the aims were, along with those of Hilbert, to understand the structure of mathematical proofs.

Chores 2009

How much of Ketonen's work stems from suggestions on the part of Gentzen remains unknown, because no correspondence has been found.

Chores 2009

The proof, among the papers of Bernays in Zurich, was discovered by the present author in February 2005 and is now available in an English translation (Gentzen 2008).

Chores 2009

After this failure, Gentzen took verbatim out of his early thesis manuscript the translation from classical to intuitionistic arithmetic and submitted it as a paper in March 1933, but withdrew the paper after hearing of Gödel's publication of the result.

Chores 2009

By early 1933, Gentzen realized that this proof strategy would not go through: the induction rule is schematic and has an infinity of instances, with no bound on the complexity of the induction formulas.

Chores 2009

At the request of Bernays, Ackermann reproduced Gentzen 'proof in terms of Hilbert's epsilon-calculus in 1940.

Chores 2009