8 citations · 20 across the 14 of their papers we have counts for
5 papers · 1 filter
Relative consistency of a finite nonclassical theory incorporating ZF and category theory with ZF
Marcoen J. T. F. Cabbolet, Adrian R. D. Mathias
Recently, in Axioms 10(2): 119 (2021), a nonclassical first-order theory T of sets and functions has been introduced as the collection of axioms we have to accept if we want a foun…
A marriage of category theory and set theory: a finitely axiomatized nonstandard first-order theory implying ZF
Marcoen J. T. F. Cabbolet
It is well known that ZFC, despite its usefulness as a foundational theory for mathematics, has two unwanted features: it cannot be written down explicitly due to its infinitely ma…
Hyperreal delta functions as a new general tool for modeling physical states with infinitely high densities
Marcoen J. T. F. Cabbolet
This paper introduces the expanded real numbers as an ordered subring of the hyperreal number field that does not contain any infinitesimals, and defines the set of all integrable…
The Importance of Developing a Foundation for Naive Category Theory
Marcoen J. T. F. Cabbolet
Recently Feferman (Rev. Symb. Logic 6: 6-15, 2013) has outlined a program for the development of a foundation for naive category theory. While Ernst (ibid. 8: 306-327, 2015) has sh…
Finitely Axiomatized Set Theory: a nonclassical first-order theory implying ZF
Marcoen Cabbolet
It is well-known that a finite axiomatization of Zermelo-Fraenkel set theory (ZF) is not possible in the same first-order language. In this note we show that a finite axiomatizatio…