A numerical technique is presented for the solution of Falkner-Skan equation. The nonlinear ordinary differential equation is solved using Chebyshev cardinal functions. The method have been derived by first truncating the semi-infinite physical domain of the problem to a finite domain and expanding the required approximate solution as the elements of Chebyshev cardinal functions. Using the oper...

In [13] it was demonstrated that the Proper Forcing Axiom implies that there is a five element basis for the class of uncountable linear orders. The assumptions needed in the proof have consistency strength of at least infinitely many Woodin cardinals. In this paper we reduce the upper bound on the consistency strength of such a basis to something less than a Mahlo cardinal, a hypothesis which ...

In this paper we investigate under what conditions is a mapping f of a semigroup S into the class of cardinals representable by a groupoid G and a homomorphism g of G onto S such that ker(g) is the associativity congruence of G and Card(g(x)) = f(x) for every x ∈ S. Abstrakt. V tomto článku vyšetřujeme, za jakých podmı́nek lze zobrazeńı f pologrupy S do tř́ıdy všech kardinálńıch č́ısel reprezentov...

We study the general problem of behaviour continuum function in presence non-supercompact strongly compact cardinals. begin by showing that it is possible to force violations GCH at an arbitrary cardinal using only strong compactness as our initial assumption. This result due third author. then investigate realising Easton functions and above least measurable limit supercompact cardinals starti...

A cardinal related to compositions of Sierpiński–Zygmund functions from the left, cleft(SZ), will be considered. We answer a question of K. Ciesielski and T. Natkaniec. In particular, we show that cl(SZ) = (2c)+ if R is not a union of less than c-many meager sets and c is a limit cardinal. If c = ω1, then cl(SZ) is equal to the bounding number of c.