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

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

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

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