by
Paola Cattabriga

Citations: | 2 - 2 self |

@MISC{Cattabriga06beyondundecidable,

author = {Paola Cattabriga},

title = {BEYOND UNDECIDABLE},

year = {2006}

}

Abstract. The predicate complementary to the well-known Gödel’s provability predicate is defined. From its recursiveness new consequences concerning the incompleteness argumentation are drawn and extended to new results of consistency, completeness and decidability with regard to Peano Arithmetic and the first order predicate calculus.

134 |
On formally undecidable propositions of Principia Mathematica and related systems I. Translated by Elliott Mendelson
- Gödel
- 1931
(Show Context)
Citation Context ... predicate, Gödel numbering. Introduction Of all the remarkable logical achievements of the twentieth century perhaps the most outstanding is the celebrated Gödel incompleteness argumentation of 1931 =-=[1, 2]-=-. In contrast to Hilbert’s program called for embodying classical mathematics in a formal system and proving that system consistent by finitary methods [4], Gödel paper showed that not even the first ... |

85 |
Grundzüge der theoretischen Logik
- Hilbert, Bernays
- 1928
(Show Context)
Citation Context ...t to be the key of the problem in defining refutability with the same recursive status as provability. The inquiry comes up with a final solution for finitary methods and the related decision problem =-=[3]-=-. The paper is organized as follows. Firstly, in the following of this section, we introduce diagonalization and the famous incompleteness argumentation of Gödel. Section 1 presents two new primitive ... |

47 |
On Undecidable Propositions of Formal Mathematical Systems, lecture notes by
- Godel
- 1934
(Show Context)
Citation Context ... predicate, Gödel numbering. Introduction Of all the remarkable logical achievements of the twentieth century perhaps the most outstanding is the celebrated Gödel incompleteness argumentation of 1931 =-=[1, 2]-=-. In contrast to Hilbert’s program called for embodying classical mathematics in a formal system and proving that system consistent by finitary methods [4], Gödel paper showed that not even the first ... |

20 |
Introduction to Mathematical Logic, Third Edition
- Mendelson
- 1987
(Show Context)
Citation Context ...or first order predicate calculus. Basic Setup. We shall assume a first order theory which adequately formalizes Peano Arithmetic (see for example the system S, with all the necessary assumptions, in =-=[5]-=- 116-175). Let us call it PA. As is well known by means of the Gödel numbering, each expression in PA can refer to itself. Numerals, as usual, are defined recursively, 0 is 0 and for any natural numbe... |

6 |
Die Grundlegung der Mathematik I
- Hilbert, Bernays
- 1934
(Show Context)
Citation Context ...ödel incompleteness argumentation of 1931 [1, 2]. In contrast to Hilbert’s program called for embodying classical mathematics in a formal system and proving that system consistent by finitary methods =-=[4]-=-, Gödel paper showed that not even the first step could be carried out fully, any formal system suitable for the arithmetic of integers was incomplete. The present article, in the most absolute respec... |

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