214 research outputs found
DeBruijn Strings, Double Helices, and the Ehrenfeucht-Mycielski Mechanism
We revisit the pseudo-random sequence introduced by Ehrenfeucht and Mycielski
and its connections with DeBruijn strings
Compactness of powers of \omega
We characterize exactly the compactness properties of the product of \kappa\
copies of the space \omega\ with the discrete topology. The characterization
involves uniform ultrafilters, infinitary languages, and the existence of
nonstandard elements in elementary estensions. We also have results involving
products of possibly uncountable regular cardinals.Comment: v2 slightly improve
DeBruijn Strings, Double Helices, and the Ehrenfeucht-Mycielski Mechanism
Abstract We revisit the pseudo-random sequence introduced by Ehrenfeucht and Mycielski and its connections with DeBruijn strings
Some attempts at a direct reduction of the infinite to the (large) finite
I survey some endeavors which have been made to attain a sort of direct reduction of the usual notion of countable infinity to some reasonable notion of finiteness, in terms of nonstandard arithmetic, feasibility, pseudo-models of derivations, Ehrenfeucht star-models, etc. I maintain that although many interesting results have been obtained in these attempts, they ultimately show that (at least by the means considered here) no satisfactory reduction is possible
On two intersecting set systems and k-continuous boolean functions
AbstractIf A and B are two systems of a-element and b-elementsets, respectively, and A ∩ B ≠Ø for A ϵ A, B ϵ B, then there exists an X, |X| $̌(a+ba), such that A ∩ B ∩ X ≠Ø for A ϵ A, B ϵ B. This estimate is sharp apart from a constant factor.As a consequence, k-continuous Boolean functions can depend on at most O((2kk)) variables
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