Church introduced λ-calculus in the beginning of the thirties as a foundation of mathematics and map theory from around 1992 fulfilled that primary aim. The present paper presents a new version of map theory whose axioms are simpler and better motivated than those of the original version from 1992. The paper focuses on the semantics of map theory and explains this semantics on basis of κ-Scott ...

be the upper density. If D < ∞ and the series (1) converges uniformly on compact subsets of the complex plane C then an = 0 for all n, [2, 3, 1]. On the other hand, there are sequences of infinite density, in fact with the quotient in the RHS of (2) growing arbitrarily slowly, such that some series (1) with non-zero coefficients converges to zero uniformly on compact subsets of C, see [2, 3, 1]...