Observations concerning Gödel's 1931

Details Observations concerning Gödel's 1931 Observations concerning Gödel's 1931

2003-06-02

arxiv.org/abs/math/0306038v9

Mathematics

General Mathematics

13 pages, for more information see http://digilander.libero.it/paola.cattabriga/

Scientific paper

This article demonstrates the invalidity of Theorem VI of Godel's monograph of 1931, showing that propositions (15) and (16), derived from definition (8.1), in its proof, are false in PA. This is achieved in two steps. First, the predicate complementary to the well-known Godel's predicate Bew(x) is ndefined by adding a new relation Wid(x), and new logical connections are accordingly established, Lemma (6). Second, the negations of (15) and (16) are derived by definition (8.1) and Lemma (6). It amounts to saying that (15) and (16) are false and unacceptable for the system. On the account of that, the two well-known cases 1. 17 Gen r is not k-PROVABLE, 2. Neg(17 Gen r) is not k-PROVABLE, can not be drawn, and Theorem VI is therefore invalid.

Affiliated with

Also associated with

No associations

Rating

Observations concerning Gödel's 1931 does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Observations concerning Gödel's 1931, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Observations concerning Gödel's 1931 will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-484870