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Generic sets in definably compact groups

Ya'acov Peterzil, Anand Pillay (2007)

Fundamenta Mathematicae

A subset X of a group G is called left genericif finitely many left translates of X cover G. Our main result is that if G is a definably compact group in an o-minimal structure and a definable X ⊆ G is not right generic then its complement is left generic. Among our additional results are (i) a new condition equivalent to definable compactness, (ii) the existence of a finitely additive invariant measure on definable sets in a definably compact group G in the case where G = *H...

Global stability of Clifford-valued Takagi-Sugeno fuzzy neural networks with time-varying delays and impulses

Ramalingam Sriraman, Asha Nedunchezhiyan (2022)

Kybernetika

In this study, we consider the Takagi-Sugeno (T-S) fuzzy model to examine the global asymptotic stability of Clifford-valued neural networks with time-varying delays and impulses. In order to achieve the global asymptotic stability criteria, we design a general network model that includes quaternion-, complex-, and real-valued networks as special cases. First, we decompose the n -dimensional Clifford-valued neural network into 2 m n -dimensional real-valued counterparts in order to solve the noncommutativity...

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

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