## Consistency of arithmetic through
sequent calculus in natural deduction style

Dept. of Philosophy

University of Helsinki

Friday, 7 May 2004, 11:00 (note the unusual weekday and time!)

Cybernetica Bldg (Akadeemia tee 21), room B101

**Abstract**: In sequent calculus in natural deduction style,
any multiplicities of active formulas can appear in the premisses of
logical rules. No structural rules are needed, because multiplicity
zero corresponds to weakening and greater than one to contraction.

Sequent calculus in natural deduction style is applied to simplify
and complete Gentzen's third (1938) consistency proof of
arithmetic.

Reference:

S. Negri, J. von Plato. Sequent calculus in natural deduction style.
J. of Symbolic Logic, v. 66, n. 4, pp. 1803-1816, 2001.

Tarmo Uustalu

Last update 25.4.2004