Predicative algebraic set theory.
Prediction problems and ultrafilters on ω
We consider prediction problems in which each of a countably infinite set of agents tries to guess his own hat color based on the colors of the hats worn by the agents he can see, where who can see whom is specified by a graph V on ω. Our interest is in the case in which 𝓤 is an ultrafilter on the set of agents, and we seek conditions on 𝓤 and V ensuring the existence of a strategy such that the set of agents guessing correctly is of 𝓤-measure one. A natural necessary condition is the absence...
Prenormality of ideals and completeness of their quotient algebras
It is well known that if a nontrivial ideal ℑ on κ is normal, its quotient Boolean algebra P(κ)/ℑ is -complete. It is also known that such completeness of the quotient does not characterize normality, since P(κ)/ℑ turns out to be -complete whenever ℑ is prenormal, i.e. whenever there exists a minimal ℑ-measurable function in . Recently, it has been established by Zrotowski (see [Z1], [CWZ] and [Z2]) that for non-Mahlo κ, not only is the above condition sufficient but also necessary for P(κ)/ℑ...
Prescribing endomorphism algebras of -free modules
It is a well-known fact that modules over a commutative ring in general cannot be classified, and it is also well-known that we have to impose severe restrictions on either the ring or on the class of modules to solve this problem. One of the restrictions on the modules comes from freeness assumptions which have been intensively studied in recent decades. Two interesting, distinct but typical examples are the papers by Blass [1] and Eklof [8], both jointly with Shelah. In the first case the authors...
Prescribing endomorphism algebras. The cotorsion-free case
Preservation of properties of fuzzy relations during aggregation processes
Diverse classes of fuzzy relations such as reflexive, irreflexive, symmetric, asymmetric, antisymmetric, connected, and transitive fuzzy relations are studied. Moreover, intersections of basic relation classes such as tolerances, tournaments, equivalences, and orders are regarded and the problem of preservation of these properties by -ary operations is considered. Namely, with the use of fuzzy relations and -argument operation on the interval , a new fuzzy relation is created. Characterization...
Preservation of the Borel class under open-LC functions
Let X be a Borel subset of the Cantor set C of additive or multiplicative class α, and f: X → Y be a continuous function onto Y ⊂ C with compact preimages of points. If the image f(U) of every clopen set U is the intersection of an open and a closed set, then Y is a Borel set of the same class α. This result generalizes similar results for open and closed functions.
Preserving P-points in definable forcing
I isolate a simple condition that is equivalent to preservation of P-points in definable proper forcing.
Preserving some properties of large cardinals under mild Cohen extensions
Primariness of some spaces of continuous functions.
Prime and maximal ideals of partially ordered sets
Prime Ideal Theorems and systems of finite character
We study several choice principles for systems of finite character and prove their equivalence to the Prime Ideal Theorem in ZF set theory without Axiom of Choice, among them the Intersection Lemma (stating that if is a system of finite character then so is the system of all collections of finite subsets of meeting a common member of ), the Finite Cutset Lemma (a finitary version of the Teichm“uller-Tukey Lemma), and various compactness theorems. Several implications between these statements...
Prime ideals yield almost maximal ideals
Principal concepts of systems fuzzification. Fuzzification of systems for technical and medical practice. I
Probability in the alternative set theory
Problemas de decisión en ambiente difuso.
Bajo un planteamiento difuso del Problema General de Decisión Unipersonal, se propone un método que permite definir una función de utilidad para este problema. Dicha función se muestra como una familia de funciones de utilidad, la cual se considera como la "utilidad difusa" que sirve para resolver el problema que se plantea en los distintos contextos.
Problems
Procesos de decisión de grupo con preferencias individuales difusas.
Products of ideals of Borel sets
Products of Lindelöf -spaces are Lindelöf – in some models of ZF
The stability of the Lindelöf property under the formation of products and of sums is investigated in ZF (= Zermelo-Fraenkel set theory without AC, the axiom of choice). It is • not surprising that countable summability of the Lindelöf property requires some weak choice principle, • highly surprising, however, that productivity of the Lindelöf property is guaranteed by a drastic failure of AC, • amusing that finite summability of the Lindelöf property takes place if either some weak choice principle...