How large are left exact functors?
How many clouds cover the plane?
The plane can be covered by n + 2 clouds iff .
How many normal measures can carry?
We show that assuming the consistency of a supercompact cardinal with a measurable cardinal above it, it is possible for to be measurable and to carry exactly τ normal measures, where is any regular cardinal. This contrasts with the fact that assuming AD + DC, is measurable and carries exactly three normal measures. Our proof uses the methods of [6], along with a folklore technique and a new method due to James Cummings.
How to handle fuzzy-quantities?
How to recognize a true Σ^0_3 set
Let X be a Polish space, and let be a sequence of hereditary subsets of K(X) (the space of compact subsets of X). We give a general criterion which allows one to decide whether is a true subset of K(X). We apply this criterion to show that several natural families of thin sets from harmonic analysis are true .
Hurewicz properties, non distinguishing convergence properties and sequence selection properties
Hurewicz scheme
Hybrid Prikry forcing
We present a new forcing notion combining diagonal supercompact Prikry forcing with interleaved extender based forcing. We start with a supercompact cardinal κ. In the final model the cofinality of κ is ω, the singular cardinal hypothesis fails at κ, and GCH holds below κ. Moreover we define a scale at κ which has a stationary set of bad points in the ground model.
Hydrological applications of a model-based approach to fuzzy set membership functions
Since the common approach to defining membership functions of fuzzy numbers is rather subjective, another, more objective method is proposed. It is applicable in situations where two models, say and , share the same uncertain input parameter . Model is used to assess the fuzziness of , whereas the goal is to assess the fuzziness of the -dependent output of model . Simple examples are presented to illustrate the proposed approach.
Hyperplanes in matroids and the axiom of choice
We show that in set theory without the axiom of choice ZF, the statement sH: “Every proper closed subset of a finitary matroid is the intersection of hyperplanes including it” implies AC, the axiom of choice for (nonempty) finite sets. We also provide an equivalent of the statement AC in terms of “graphic” matroids. Several open questions stay open in ZF, for example: does sH imply the axiom of choice?
Hyperstructures Associated with Ordered sets
I teoremi di assolutezza in teoria degli insiemi: prima parte
Questa è la prima parte di una articolo espositivo dedicato ai teoremi di assolutezza, un argomento che sta assumendo un’importanza via via più grande in teoria degli insiemi. In questa prima parte vedremo come le questioni di teoria dei numeri non siano influenzate da assunzioni insiemistiche quali l’assioma di scelta o l’ipotesi del continuo.
I teoremi di assolutezza in teoria degli insiemi: seconda parte
Questa è la seconda parte dell’articolo espositivo [A]. Qui vedremo come siapossibile utilizzare il forcinge gli assiomi forti dell’infinito per dimostrare nuovi teoremi sui numeri reali.
Ideal limits of sequences of continuous functions
We prove that for every Borel ideal, the ideal limits of sequences of continuous functions on a Polish space are of Baire class one if and only if the ideal does not contain a copy of Fin × Fin. In particular, this is true for ideals. In the proof we use Borel determinacy for a game introduced by C. Laflamme.
Ideals induced by Tsirelson submeasures
We use Tsirelson’s Banach space ([2]) to define an P-ideal which refutes a conjecture of Mazur and Kechris (see [12, 9, 8]).
Ideals of the second category
Ideals on the real line and Ulam's problem
Ideals which generalize (v 0)
Countable products of finite discrete spaces with more than one point and ideals generated by Marczewski-Burstin bases (assigned to trimmed trees) are examined, using machinery of base tree in the sense of B. Balcar and P. Simon. Applying Kulpa-Szymanski Theorem, we prove that the covering number equals to the additivity or the additivity plus for each of the ideals considered.
Idempotence de l'opération de souslin
Idempotent and compact matrices on linear lattices: A survey of some lattice results and related solutions of finite relational equations.