Set Theory and Logic

2410 Submissions

[3] viXra:2410.0151 [pdf] replaced on 2026-01-11 11:11:44

Understanding Universal Disjunction

Authors: Garry Goodwin
Comments: 9 Pages.

The difference in meaning between the two versions of universal disjunction is rarely subjected to systematic analysis. We identify and examine twelve distinct interpretations that allow us to distinguish individually quantified disjoint sentences from cases in which the universal quantifier is distributed over a disjunction.}
Category: Set Theory and Logic

[2] viXra:2410.0123 [pdf] submitted on 2024-10-21 04:32:35

A Pathology of the Von Neumann Ordinals

Authors: David L. Selke
Comments: 4 Pages.

We show that the definition of the Von Neumann ordinal $omega_2$ fails to have the properties of an ordinal. In the notation that uses braces to denote ordinals, the ``depth" or ``height" of nesting of these braces becomes infinite leading to objects which have no top level of braces and which therefore have their elements undefined, leading to the conclusion that they are not sets at all, let alone ordinals. The least of these objects occurs before (that is, within) $omega_2$.
Category: Set Theory and Logic

[1] viXra:2410.0083 [pdf] submitted on 2024-10-15 23:40:43

Formalizing Mechanical Analysis Using Sweeping Net Methods

Authors: Parker Emmerson
Comments: 12 Pages.

We present a formal mechanical analysis using sweeping net methods to approximate surfacingsingularities of saddle maps. By constructing densified sweeping subnets for individual vertices and integrating them, we create a comprehensive approximation of singularities. This approach utilizes geometric concepts, analytical methods, and theorems that demonstrate the robustness and stabilityof the nets under perturbations. Through detailed proofs and visualizations, we provide a new perspective on singularities and their approximations in analytic geometry.
Category: Set Theory and Logic