Combinatory interpolation theorems

Generalized Interpolation Theorems

(Note that the Craig interpolation theorem is the special case of Chang's theorem in which Q19,.., Qn are all universal quantifiers.) Chang also raised the question [2, Remark (k)] as to whether the Lopez-Escobar interpolation theorem [6] for the infinitary language L.1. possesses a similar generalization. In this paper, we show that the answer to Chang's question is affirmative and, moreover, ...

Interpolation theorems in jump graphs

Interpolation Theorems on Graph Parameters

For each graph parameter f = f(G) of a graph G, it is said that f interpolates over the set of all graphs with a fixed degree sequence d,R(d) if the following statement holds: If m and M are the minimum and maximum values (respectively) of f(G) over all G ∈ R(d), then for any k, m ≤ k ≤ M, there is a graph G ∈ R(d) such that f(G) = k. In this paper, three graph parameters are shown to be interp...

A New Look at Localic Interpolation Theorems

Abstract: This paper presents a new treatment of the localic Katětov-Tong interpolation theorem, based on an analysis of special properties of normal frames, which shows that it does not hold in full generality. Besides giving us the conditions under which the localic Katětov-Tong interpolation theorem holds, this approach leads to a especially transparent and succint proof of it. It is also sh...

Some theorems and remarks on interpolation

Throughout this paper x"'), x-"1 ,. . ., x~,' will denote the roots of the n-th Chebyshev polynomial T " (x) [T " (cosh) = cos nJ]. f(x) will denote a function continuous in [-1, +1] and L,(f(x)) will denote the Lagrange interpolation polynomial of f(x) taken at the points xi(") (i = 1, 2,. . ., n) ; in other words, L,(f(x)) is a polynomial of degree not greater than (n-1) for which') L " (f(x+...