...-Categorical Stable Groups.
...-definable functionals and ... Conversion.
...-definierbare Funktionen auf Peanoalgebren.
“Disorder” in lattices of binumerations
“Hidden variables” on concrete logics (extensions)
...-inaccessible ordinals, collapsing functions and a recursive notation system.
...-kompakte Räume.
-sums and the Banach space
This paper is concerned with the isomorphic structure of the Banach space and how it depends on combinatorial tools whose existence is consistent with but not provable from the usual axioms of ZFC. Our main global result is that it is consistent that does not have an orthogonal -decomposition, that is, it is not of the form for any Banach space X. The main local result is that it is consistent that does not embed isomorphically into , where is the cardinality of the continuum, while ...
�?lgebras de Hilbert n-valentes
♣-like principles under CH
Some relatives of the Juhász Club Principle are introduced and studied in the presence of CH. In particular, it is shown that a slight strengthening of this principle implies the existence of a Suslin tree in the presence of CH.
"Paradoxe" Zerlegung Euklidischer Räume.
(Pure) logic out of probability.
Today, Logic and Probability are mostly seen as independent fields with a separate history and set of foundations. Against this dominating perception, only a very few people (Laplace, Boole, Peirce) have suspected there was some affinity or relation between them. The truth is they have a considerable common ground which underlies the historical foundation of both disciplines and, in this century, has prompted notable thinkers as Reichenbach [14], Carnap [2] [3] or Popper [12] [13] (and Gaifman [5],...
ℳ-rank and meager groups
Assume p* is a meager type in a superstable theory T. We investigate definability properties of p*-closure. We prove that if T has countable models then the multiplicity rank ℳ of every type p is finite. We improve Saffe’s conjecture.
ℳ-rank and meager types
Assume T is superstable and small. Using the multiplicity rank ℳ we find locally modular types in the same manner as U-rank considerations yield regular types. We define local versions of ℳ-rank, which also yield meager types.
...-Strukturen.
‘Sur le concept de nombre en mathématique’ Cours inédit de Leopold Kronecker à Berlin (1891)
Le texte que nous présentons est le dernier cours du mathématicien berlinois Leopold Kronecker (1823–1891). Ce cours, publié ici pour la première fois, nous donne des informations importantes sur la philosophie des mathématiques de Kronecker, en particulier sur sa conception du nombre. Il précise, en outre, la position que Kronecker occupa dans le mouvement d’‘arithmétisation’ des mathématiques et permet de mieux comprendre comment, et pourquoi, il se situe à contre-courant de la tendance dominante...
(T, ⊥, N) fuzzy logic.
To investigate more reasonable fuzzy reasoning model in expert systems as well as more effective logical circuit in fuzzy control, a (T, ⊥, N) fuzzy logic is proposed in this paper by using T-norm, ⊥-norm and pseudo-complement N as the logical connectives. Two aspects are discussed: (1) some concepts of (T, ⊥, N) fuzzy logic are introduced and some properties of (T, ⊥, N) fuzzy logical formulae are discussed. (2) G-fuzzy truth (falsity) of (T, ⊥, N) fuzzy logical formulae are investigated and also...
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-filters and -order-ideals in distributive quasicomplemented semilattices
We introduce some particular classes of filters and order-ideals in distributive semilattices, called -filters and -order-ideals, respectively. In particular, we study -filters and -order-ideals in distributive quasicomplemented semilattices. We also characterize the filters-congruence-cokernels in distributive quasicomplemented semilattices through -order-ideals.