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Gödel et la thèse de Turing

Pierre Cassou-Noguès (2008)

Revue d'histoire des mathématiques

Cet article porte sur la discussion par Gödel de la thèse de Turing. Pour l’essentiel, nous présentons des notes inédites conservées dans les Archives Gödel, qui apportent des éléments nouveaux sur la relation ambiguë de Gödel à Turing. La première section examine la position qu’avait Gödel avant 1937 sur la possibilité d’une définition de la calculabilité. La deuxième concerne directement l’interprétation par Gödel de la thèse de Turing. Dans plusieurs passages, antérieurs à 1937, Gödel qualifie...

Goldstern–Judah–Shelah preservation theorem for countable support iterations

Miroslav Repický (1994)

Fundamenta Mathematicae

[1] T. Bartoszyński, Additivity of measure implies additivity of category, Trans. Amer. Math. Soc. 281 (1984), 209-213. [2] T. Bartoszyński and H. Judah, Measure and Category, in preparation. [3] D. H. Fremlin, Cichoń’s diagram, Publ. Math. Univ. Pierre Marie Curie 66, Sém. Initiation Anal., 1983/84, Exp. 5, 13 pp. [4] M. Goldstern, Tools for your forcing construction, in: Set Theory of the Reals, Conference of Bar-Ilan University, H. Judah (ed.), Israel Math. Conf. Proc. 6, 1992, 307-362. [5] H....

Good choice sets

J. C. E. Dekker (1966)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Graded sets, points and numbers.

José A. Herencia (1998)

Mathware and Soft Computing

The basic tool considered in this paper is the so-called graded set, defined on the analogy of the family of α-cuts of a fuzzy set. It is also considered the corresponding extensions of the concepts of a point and of a real number (again on the analogy of the fuzzy case). These new graded concepts avoid the disadvantages pointed out by Gerla (for the fuzzy points) and by Kaleva and Seikkala (for the convergence of sequences of fuzzy numbers).

Group of Homography in Real Projective Plane

Roland Coghetto (2017)

Formalized Mathematics

Using the Mizar system [2], we formalized that homographies of the projective real plane (as defined in [5]), form a group. Then, we prove that, using the notations of Borsuk and Szmielew in [3] “Consider in space ℝℙ2 points P1, P2, P3, P4 of which three points are not collinear and points Q1,Q2,Q3,Q4 each three points of which are also not collinear. There exists one homography h of space ℝℙ2 such that h(Pi) = Qi for i = 1, 2, 3, 4.” (Existence Statement 52 and Existence Statement 53) [3]. Or,...

Groups – Additive Notation

Roland Coghetto (2015)

Formalized Mathematics

We translate the articles covering group theory already available in the Mizar Mathematical Library from multiplicative into additive notation. We adapt the works of Wojciech A. Trybulec [41, 42, 43] and Artur Korniłowicz [25]. In particular, these authors have defined the notions of group, abelian group, power of an element of a group, order of a group and order of an element, subgroup, coset of a subgroup, index of a subgroup, conjugation, normal subgroup, topological group, dense subset and basis...

Group-valued measures on coarse-grained quantum logics

Anna de Simone, Pavel Pták (2007)

Czechoslovak Mathematical Journal

In it was shown that a (real) signed measure on a cyclic coarse-grained quantum logic can be extended, as a signed measure, over the entire power algebra. Later () this result was re-proved (and further improved on) and, moreover, the non-negative measures were shown to allow for extensions as non-negative measures. In both cases the proof technique used was the technique of linear algebra. In this paper we further generalize the results cited by extending group-valued measures on cyclic coarse-grained...

Grzegorczyk’s Logics. Part I

Taneli Huuskonen (2015)

Formalized Mathematics

This article is the second in a series formalizing some results in my joint work with Prof. Joanna Golinska-Pilarek ([9] and [10]) concerning a logic proposed by Prof. Andrzej Grzegorczyk ([11]). This part presents the syntax and axioms of Grzegorczyk’s Logic of Descriptions (LD) as originally proposed by him, as well as some theorems not depending on any semantic constructions. There are both some clear similarities and fundamental differences between LD and the non-Fregean logics introduced by...

Guessing clubs in the generalized club filter

Bernhard König, Paul Larson, Yasuo Yoshinobu (2007)

Fundamenta Mathematicae

We present principles for guessing clubs in the generalized club filter on κ λ . These principles are shown to be weaker than classical diamond principles but often serve as sufficient substitutes. One application is a new construction of a λ⁺-Suslin-tree using assumptions different from previous constructions. The other application partly solves open problems regarding the cofinality of reflection points for stationary subsets of [ λ ] ℵ ₀ .

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