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- Witold Marciszewski, Greg Chaitin, Richard J. Gaylor, Louis J. D’Andria
- 2003

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)

An internal characterization of metric spaces which are absolute Borel sets of multiplicative classes is given. This characterization uses complete sequences of covers, a notion introduced by Frolík for characterizingČech-complete spaces. We also show that the absolute Borel class of X is determined by the uniform structure of the space of continuous… (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)

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)

- Murray Bell, Witold Marciszewski
- J. Symb. Log.
- 2006

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)

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