December 13
Cezary Cieśliński,
University of Warsaw
On the principle of disjunctive correctness
The disjunctive correctness principle (DC) states that a disjunction of arbitrary (possibly nonstandard) length is true if and only if one of its disjuncts is true. On first sight, the principle seems an innocent and natural generalization of the familiar compositional truth axiom for disjunction. However, Ali Enayat and Fedor Pakhomov demonstrated that (DC) has the same strength as Delta_0 induction, hence it produces a non-conservative extension of the background arithmetical theory.
In the presentation the proof of a stronger result will be presented. Let (DC-Elim) be just one direction of (DC), namely, the implication 'if a disjunction is true, then one of it disjuncts is true'. We will show that already (DC-Elim) carries the full strength of Delta_0 induction; moreover, the proof of this fact will be significantly simpler than the original argument of Enayat and Pakhomov.