Recently published in Logica Universalis: "Gödel’s Ontological Proof and its Consistency Consequences" Piergiorgio Odifreddi & Thiago Gomes Abstract: This paper examines the ultrafilter interpretation of Kurt Gödel’s ontological argument and explores its philosophical and mathematical consequences. After reviewing the formulations of Anselm of Canterbury, Gottfried Wilhelm Leibniz, and Gödel, we show how Gödel’s positivity axioms can be understood extensionally as defining an ultrafilter over the domain of individuals. We argue that this perspective sheds new light on the modal collapse, suggesting that it reflects not merely features of the modal framework, but deeper structural properties of the underlying ultrafilter. We then relate this interpretation to the work of Harvey Friedman, where non-principal ultrafilters and divine objects are used to obtain relative consistency results in set theory. https://link.springer.com/article/10.1007/s11787-026-00409-6
This paper is published in open access. Springer Nature has agreements with many countries/institutions so that researchers can publish in open access for free, see e.g. for the USA: https://www.springernature.com/gp/open-science/oa-agreements/usa Everybody is welcome to submit a paper to Logica Universalis, which I founded in 2007, and in which papers by highly distinguished logicians such as Johan van Benthem, Solomon Feferman, Dov Gabbay, Rohit Parikh, and Jaakko Hintikka have already been published, to mention just five names, as well as papers by the prize winners from each country in the first three editions of the World Logic Prizes Contest: 1st edition, 6th UNILOG, Vichy, June 2018 https://link.springer.com/journal/11787/volumes-and-issues/12-3 2nd Edition, 7th UNILOG, Crete, April 2022 https://link.springer.com/journal/11787/volumes-and-issues/16-1 3rd Edition, 8th UNILOG, Cusco, December, 2025 https://link.springer.com/journal/11787/volumes-and-issues/19-4 >-------------------------------------------------------------------- Jean-Yves Beziau Founder and Editor-in-Chief Logica Universalis https://philpeople.org/profiles/jean-yves-beziau
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