In the paper we formulate a Covering Property Axiom CPA cube , which holds in the iterated perfect set model, and show that it implies the existence of uncountable strong γ-sets in R (which are strongly meager) as well as uncountable γ-sets in R which are not strongly meager. These sets must be of cardinality ω1 < c, since every γ-set is universally null, while CPA cube implies that every unive...

The subject of this article is a description of Polish inflection in the form of a relational database. The description has been developed for a grammatical dictionary of Polish that aims at complete inflectional characterisation of all Polish lexemes. We show some complexities of the Polish inflectional system for various grammatical classes. Then we present a relatively compact relational mod...

We prove that the Covering Property Axiom CPAprism, which holds in the iterated perfect set model, implies the following facts. • There exists a family G of uniformly continuous functions from R to [0, 1] such that |G| = ω1 and for every S ∈ [R] there exists a g ∈ G with g[S] = [0, 1]. • The additivity of the Marczewski’s ideal s0 is equal to ω1 < c. 1 Preliminaries and axiom CPAprism Our set t...

Wadge reducibility provides a rich and nice analysis of Borel sets in Polish zero dimensional spaces. However, outside this framework, reducibility by continuous functions was shown to be ill behaved in many important cases. We define a notion of reducibility for subsets of a second countable T0 topological space based on the notions of admissible representations and relatively continuous relat...

Contents Chapter 1. Martingales, continued 1 1.1. Martingales indexed by partially ordered sets 1 1.2. Notions of convergence for martingales 3 1.3. Uniform integrability 4 1.4. Convergence of martingales with directed index sets 6 1.5. Application: The 0-1 law of Kolmogorov 8 1.6. Continuous-time martingales 9 1.7. Tail bounds for martingales 12 1.8. Application: The Pólya urn 13 1.9. Applicat...

What should it mean for us to say that two distributions are close, or that a sequence μn of distributions of some random variables Xn taking values in some state space X converges to another distribution μ of some random variable X? Certainly we’ll need to know if Xn and X are close, so we’ll restrict ourselves to state spaces X that are sigma-compact metric spaces (and to avoid needless techn...

2013 | Volume19 | Issue 3 | 17 The article presents biomedical experiments conducted by the fi rst Polish cosmonaut, Maj. Mirosław Hermaszewski, with consideration being paid to the conditions and scientifi c importance of the experiments. Three experiments developed by Polish researchers, titled “Zdrowie” (“Health”), “Kardiolider” (“Cardioleader”) and “Smak” (“Taste”) are presented in detail. ...

This paper describes the rapid development of a Polish language speech recognition system. The system development was performed without access to any transcribed acoustic training data. This was achieved through the combined use of cross-language bootstrapping and confidence based unsupervised acoustic model training. A Spanish acoustic model was ported to Polish, through the use of a manually ...

A topological group G is defined to have property (OB) if any G-action by isometries on a metric space, which is separately continuous, has bounded orbits. We study this topological analogue of strong uncountable cofinality in the context of Polish groups, where we show it to have several interesting reformulations and consequences. We subsequently apply the results obtained in order to verify ...