Definitions of finite
Definitions of finiteness based on order properties
A definition of finiteness is a set-theoretical property of a set that, if the Axiom of Choice (AC) is assumed, is equivalent to stating that the set is finite; several such definitions have been studied over the years. In this article we introduce a framework for generating definitions of finiteness in a systematical way: basic definitions are obtained from properties of certain classes of binary relations, and further definitions are obtained from the basic ones by closing them under subsets...
Definitions: the primitive concept of logics or The Leśniewski-Tarski legacy [Book]
Definizione dei clan binari e loro classificazione
L’albero binario (libero) è una struttura analoga a quella dei numeri naturali (standard), salvo che ci sono due operazioni di successivo. Nello studio degli alberi binari non standard, si ha bisogno di strutture ordinate che stiano a quella di albero binario libero come la struttura (ordinata) Z sta ad N. Si introducono perciò i clan binari e se ne studiano le classi di isomorfismo. Si dimostra che esse sono determinate dalle classi di similitudine delle successioni numerabili di 2 elementi, avendo...
Degradation in probability logic: When more information leads to less precise conclusions
Probability logic studies the properties resulting from the probabilistic interpretation of logical argument forms. Typical examples are probabilistic Modus Ponens and Modus Tollens. Argument forms with two premises usually lead from precise probabilities of the premises to imprecise or interval probabilities of the conclusion. In the contribution, we study generalized inference forms having three or more premises. Recently, Gilio has shown that these generalized forms “degrade” – more premises...
Degrees of dependence in the theory of semisets.
Degrees of interpretability
Degrees of non-definability of the Sacks model
Degrees of unsolvability within a regressive isol
Degree-theoretic bounds on the Morley rank.
Demonic semantics: using monotypes and residuals.
Dénombrements relatifs à une définition combinatoire de la continuité sur un graphe
Dénombrements systématiques de relations binaires externes
Denotational aspects of untyped normalization by evaluation
We show that the standard normalization-by-evaluation construction for the simply-typed -calculus has a natural counterpart for the untyped -calculus, with the central type-indexed logical relation replaced by a “recursively defined” invariant relation, in the style of Pitts. In fact, the construction can be seen as generalizing a computational-adequacy argument for an untyped, call-by-name language to normalization instead of evaluation.In the untyped setting, not all terms have normal forms,...
Denotational aspects of untyped normalization by evaluation
We show that the standard normalization-by-evaluation construction for the simply-typed λβη-calculus has a natural counterpart for the untyped λβ-calculus, with the central type-indexed logical relation replaced by a “recursively defined” invariant relation, in the style of Pitts. In fact, the construction can be seen as generalizing a computational-adequacy argument for an untyped, call-by-name language to normalization instead of evaluation.In the untyped setting, not all terms have normal...
Dense orderings, partitions and weak forms of choice
We investigate the relative consistency and independence of statements which imply the existence of various kinds of dense orders, including dense linear orders. We study as well the relationship between these statements and others involving partition properties. Since we work in ZF (i.e. without the Axiom of Choice), we also analyze the role that some weaker forms of AC play in this context
Dense pairs of o-minimal structures
The structure of definable sets and maps in dense elementary pairs of o-minimal expansions of ordered abelian groups is described. It turns out that a certain notion of "small definable set" plays a special role in this description.
Densité et dimension
Une partie de est appelée une classe de Vapnik-Cervonenkis si la croissance de la fonction est polynomiale; ces classes se trouvent être utiles en Statistique et en Calcul des Probabilités (voir par exemple Vapnik, Cervonenkis [V.N. Vapnik, A.YA. Cervonenkis, Theor. Prob. Appl., 16 (1971), 264-280], Dudley [R.M. Dudley, Ann. of Prob., 6 (1978), 899-929]).Le présent travail est un essai de synthèse sur les classes de Vapnik-Cervonenkis. Mais il contient aussi beaucoup de résultats nouveaux,...
Dependences between definitions of finiteness
Dependences between definitions of finiteness. II