A new axiom is proposed, the Ground Axiom, asserting that the universe is not a nontrivial set forcing extension of any inner model. The Ground Axiom is first-order expressible, and any model of zfc has a class forcing extension which satisfies it. The Ground Axiom is independent of many well-known set-theoretic assertions including the Generalized Continuum Hypothesis, the assertion v=hod that...

Development of new algorithms in the area machine learning, especially clustering, comparative studies such as well testing according to software engineering principles requires availability labeled data sets. While standard benchmarks are made available, a broader range sets is necessary order avoid problem overfitting. In this context, theoretical works on axiomatization clustering algorithms...

Previously, the authors used insights of Robinson's nonstandard analysis as a powerful tool to extend and simplify construction some compactifications regular spaces. They now show that any Hausdorff compactification is obtainable with their method.

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...