Glivenko's theorems from an ecumenical perspective

Luiz Carlos Pereira; Victor Barroso-Nascimento; Elaine Pimentel

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arXiv · 2605.02450

Glivenko's theorems from an ecumenical perspective

Luiz Carlos Pereira·Victor Barroso-Nascimento·Elaine Pimentel

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Abstract

In this paper, we revisit Glivenko's theorems, foundational results relating classical and intuitionistic logic, from an ecumenical perspective. We begin by discussing the historical context and significance of Glivenko's original contributions, and then examine their extensions and reinterpretations within ecumenical logical frameworks. Our analysis focuses on three ecumenical systems: Prawitz's natural deduction system NE; the system NEK, closely related to one introduced by Krauss in an unpublished manuscript; and the ECI system proposed by Barroso-Nascimento.

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Luiz Carlos Pereira, Victor Barroso-Nascimento, Elaine Pimentel. 2026-05-04. Glivenko's theorems from an ecumenical perspective. https://arxiv.org/abs/2605.02450

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