Witold Marciszewski

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We prove that if X is a countable nondiscrete completely regular space such that the function space C (X) is an absolute FaS-set, then C (X) is homeomorphic to <7°° , where a = {(x¡) e R00:*, = 0 for all but finitely many i} . As an application we answer in the negative some problems of A. V. Arhangel'skii by giving examples of countable completely regular(More)
Motto One: There are actually lots of threads that led to computer technology, which come from mathematical logic and from philosophical questions about the limits and the power of mathematics. Motto Two: Computer simulations are extremely useful in the social sciences. It provides a laboratory in which qualitative ideas about social and economic(More)
We announce a complete topological classification of the function spaces C (X) of Borel class not higher than 2, provided that I is a countable space. We also present a topological classification of the /c-dimensional universal pseu-doboundaries and pseudointeriors in R n , and we investigate under what conditions strong negligibility of crZ-sets(More)
On going beyond the first-order logic in testing the validity of its formulas A case study 1. Let us fancy for a moment that the first-order logic (FOL) is decidable. And let the famous Gödelian sentence (G) about its own unprovability, after its encoding in the language of arithmetic , be put as the consequent in the conditional whose antecedent is(More)
Gödelian speed-up is a handy concept when dealing with decidability and tractability, even if it did not become common in logical literature yet. 1 Since the phrase " decidability and tractability " , when uttered in one breath (as we shall often do), is a bit clumsy, let it be shortened for " D&T ". In this pair, the theoretical (or, in principle)(More)
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