Definable Ultrapowers and the Omitting Types Theorem
Definably complete Baire structures
We consider definably complete Baire expansions of ordered fields: every definable subset of the domain of the structure has a supremum and the domain cannot be written as the union of a definable increasing family of nowhere dense sets. Every expansion of the real field is definably complete and Baire, and so is every o-minimal expansion of a field. Moreover, unlike the o-minimal case, the structures considered form an axiomatizable class. In this context we prove a version of the Kuratowski-Ulam...
...-definierbare Funktionen auf Peanoalgebren.
Definierbare Funktionen im ...-Kalkül mit Typen.
Defining cardinal addition by ≤-formulas
Definition and Properties of Direct Sum Decomposition of Groups1
In this article, direct sum decomposition of group is mainly discussed. In the second section, support of element of direct product group is defined and its properties are formalized. It is formalized here that an element of direct product group belongs to its direct sum if and only if support of the element is finite. In the third section, product map and sum map are prepared. In the fourth section, internal and external direct sum are defined. In the last section, an equivalent form of internal...
Definition of First Order Language with Arbitrary Alphabet. Syntax of Terms, Atomic Formulas and their Subterms
Second of a series of articles laying down the bases for classical first order model theory. A language is defined basically as a tuple made of an integer-valued function (adicity), a symbol of equality and a symbol for the NOR logical connective. The only requests for this tuple to be a language is that the value of the adicity in = is -2 and that its preimage (i.e. the variables set) in 0 is infinite. Existential quantification will be rendered (see [11]) by mere prefixing a formula with a letter....
Definition of Flat Poset and Existence Theorems for Recursive Call
This text includes the definition and basic notions of product of posets, chain-complete and flat posets, flattening operation, and the existence theorems of recursive call using the flattening operator. First part of the article, devoted to product and flat posets has a purely mathematical quality. Definition 3 allows to construct a flat poset from arbitrary non-empty set [12] in order to provide formal apparatus which eanbles to work with recursive calls within the Mizar langauge. To achieve this...
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