Gordon Discusses The Continuum Hypothesis.

Professor Evgeny Gordon spoke in the department colloquium on February 18th and 25-th the abstract of the talk follows:

L.V. Kantorovich, who is mostly known for the discovery of Linear Programming, was also an outstanding expert in functional analysis. He introduced and investigated conditionally order
complete vector lattices that are known in Russian mathematical literature as Kantorovich's spaces (K-spaces).

He came to these spaces in early 30's guided by the idea to find vector spaces that have as many properties of the field of real numbers as possible. At that time this problem couldn't be written in formal mathematical terms.

In the middle of 60's P. Cohen proved the independence of CH. The method of forcing that he developed for this problem was later rewritten in terms of Boolean-valued models of set theory by D. Scott and R. Solovay. In the middle of 70's I proved that Boolean-valued models of the field of real numbers are exactly the universal K-spaces. This fact did not only give a rigorous mathematical formulation to the problem of Kantorovich, but also allowed to transfer many properties of real numbers to K-spaces. In particular, it allowed generalizing a lot of theorems about linear functionals on operators with the values in Kantorovich spaces.

Many results in this area were obtained by functional analysts from Novosibirsk.