We prove the topological (or combinatorial) rigidity property for real polynomials with all critical points real and nondegenerate, which completes the last step in solving the density of Axiom A conjecture in real one-dimensional dynamics.

The purpose of this note is introduce a new axiom (called the Descent Axiom) in the theory of r-spin cohomological field theories. This axiom explains the origin of gravitational descendants in this theory. Furthermore, the Descent Axiom immediately implies the Vanishing Axiom, explicating the latter (which has no a priori analog in the theory of Gromov-Witten invariants), in terms of the multi...

we study different completeness definitions for two categories of lattice-valued cauchy spaces and the relations between these definitions. we also show the equivalence of a so-called completion axiom and the existence of a completion.

Nominalistic Logic (NL) is a new presentation of Paul Gilmore’s Intensional Type Theory (ITT) as a sequent calculus together with a succinct nominalization axiom (N) that permits names of predicates as individuals in certain cases. The logic has a flexible comprehension axiom, but no extensionality axiom and no infinity axiom, although axiom N is the key to the derivation of Peano’s postulates ...

In this paper we describe an experiment in which MANIFOLD is used to coordinate the interprocess communication in a parallelized proposition solver. MANIFOLD is very well suited for applications involving dynamic process creation and dynamically changing (ir)regular communication patterns among sets of independent concurrent cooperating processes. The idea in this case study is simple. The prop...

Veblen has given a set of axioms for geometry.!. The first eight of these are as follows : % Axiom I. There exist at least two distinct points. Axiom II. If points A, B, C are in the order ABC, they are in the order CBA. Axiom III. If points A, B, C are in the order ABC, they are not in the order BCA. Axiom IV. If points A, B, C are in the order ABC, then A is distinct from C. Axiom V. If A and...