4 papers
A Constructive Field of Infinitesimals: Chunk and Permeate Approach
Anggha Nugraha
While intuitive, naïve infinitesimal reasoning is classically inconsistent, and rigorous nonstandard analysis relies on non-constructive machinery. We resolve this tension by const…
Paraconsistent Dominated Convergence
Anggha Nugraha
The Levi-Civita field of formal Laurent series is a constructive, non-Archimedean ordered field that supports a full Lebesgue measure and integration theory, includin…
Inductive Satisfiability Certification for Universal Quantifiers and Uninterpreted Function Symbols
Stefan Ratschan, Anggha Nugraha, Mikoláš Janota +1
The combination of uninterpreted function symbols and universal quantification occurs in many applications of automated reasoning, for example, due to their ability to reason about…
Naïve Infinitesimal Analysis: Its Construction and Its Properties
Anggha Nugraha, Maarten McKubre-Jordens, Hannes Diener
This paper aims to build a new understanding of the nonstandard mathematical analysis. The main contribution of this paper is the construction of a new set of numbers, $\mathbb{R}^…