What question did this study set out to answer?

The study aims to establish a formal axiomatic system for arithmetic using minimal operations.

June 2, 2026Open Access

VR. A Formal System: A Minimalist Axiomatization of Arithmetic from Operations Alone

View Full Paper

Ask AI

Bookmark

Authors

Formal system VR constructs arithmetic foundations with operations, showing consistency relative to ZF set theory.

The study aims to establish a formal axiomatic system for arithmetic using minimal operations.
Introduced a formal system VR with primitives ∅, →, and t and defined axioms accordingly.
Constructed von Neumann natural numbers using the succession operator t and defined equality through Leibniz's principle.
Demonstrated that VR is equivalent to Peano arithmetic, supporting its consistency with ZF set theory.
Confirmed that VR is arithmetically equivalent to Peano arithmetic (PA).
Established the consistency of VR when considered relative to ZF set theory.

Vitaly Reznik (2026) studied this question.

View Full Paper

Ask AI

Bookmark

June 2, 2026Open Access

View Full Paper

Ask AI

Bookmark

Authors

Formal system VR constructs arithmetic foundations with operations, showing consistency relative to ZF set theory.

The study aims to establish a formal axiomatic system for arithmetic using minimal operations.
Introduced a formal system VR with primitives ∅, →, and t and defined axioms accordingly.
Constructed von Neumann natural numbers using the succession operator t and defined equality through Leibniz's principle.
Demonstrated that VR is equivalent to Peano arithmetic, supporting its consistency with ZF set theory.
Confirmed that VR is arithmetically equivalent to Peano arithmetic (PA).
Established the consistency of VR when considered relative to ZF set theory.

Vitaly Reznik (2026) studied this question.

View Full Paper

Ask AI

Bookmark