We derive author's discrete forms of the Beckman-Quarles theorem from the definability results of Raphael M. Robinson. The classical Beckman-Quarles theorem states that each map from R n to R n (n > 1) preserving all unit distances is an isometry, see [1]-[3]. In this note we derive author's discrete forms of this theorem ([6]) from the definability results of Raphael M. Robinson (see [4] and a...

We derive author's discrete forms of the Beckman-Quarles theorem from the definability results of Raphael M. Robinson. The classical Beckman-Quarles theorem states that each map from R n to R n (n > 1) preserving all unit distances is an isometry, see [1]-[3]. In this note we derive author's discrete forms of this theorem ([6]) from the definability results of Raphael M. Robinson (see [4] and a...

Using a convergence theorem for Fourier-Padé approximants constructed from orthogonal polynomials on the unit circle, we prove an analogue of Hadamard’s theorem for determining the radius of m-meromorphy of a function analytic on the unit disk and apply this to the location of poles of the reciprocal of Szegő functions.

In the Böhm theorem workshop on Crete island, Zoran Petric called Statman’s “Typical Ambiguity theorem” typed Böhm theorem. Moreover, he gave a new proof of the theorem based on set-theoretical models of the simply typed lambda calculus. In this paper, we study the linear version of the typed Böhm theorem on a fragment of Intuitionistic Linear Logic. We show that in the multiplicative fragment ...

In the Böhm theorem workshop on Crete island, Zoran Petric called Statman’s “Typical Ambiguity theorem” typed Böhm theorem. Moreover, he gave a new proof of the theorem based on set-theoretical models of the simply typed lambda calculus. In this paper, we study the linear version of the typed Böhm theorem on a fragment of Intuitionistic Linear Logic. We show that in the multiplicative fragment ...

We study the assignment of discrete resources in a general model encompassing wide range applied environments, such as school choice, course allocation, and refugee resettlement. allow single-unit multi-unit demands any linear constraints. prove Second Welfare Theorem for these environments strong version First Theorem. In this way, we establish an equivalence between efficiency decentralizatio...

A consistency criteria is given for a certain class of finite positive measures on the surfaces of the finite dimensional unit balls in a real separable Hilbert space. It is proved, through a Kolmogorov type existence theorem, that the class induces a unique positive measure on the surface of the unit ball in the Hilbert space. As an application, this will naturally accomplish the work of Kante...