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G\"{o}del-type universes in unimodular gravity
R. Raimarda, A. F. Santos, R. Bufalo
https://arxiv.org/abs/2506.11717 https://arx…

Gödel-type universes in unimodular gravity
In this paper, the Gödel-type universes are examined within the framework of unimodular gravity. Since the existence of Gödel solutions is intrinsically related to the presence of a cosmological constant in general relativity, one can naturally wonder how the acausal structure of the Gödel solutions behaves in different cosmological scenarios. One of the simplest, but important, frameworks within this context is the unimodular gravity, in which the cosmological constant emerges as an integra…

Matching logic -- proof system $\mathcal{G}^c$
Lauren\c{t}iu Leu\c{s}tean, Dafina Trufa\c{s}
https://arxiv.org/abs/2506.13801 https://

Matching logic -- proof system $\mathcal{G}^c$
We propose in these notes a new proof system for first-order matching logic with application, obtained by adapting to matching logic Gödel's proof system for first-order intuitionistic logic.

This https://arxiv.org/abs/2410.04444 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csAI_…

Gödel Agent: A Self-Referential Agent Framework for Recursive Self-Improvement
The rapid advancement of large language models (LLMs) has significantly enhanced the capabilities of AI-driven agents across various tasks. However, existing agentic systems, whether based on fixed pipeline algorithms or pre-defined meta-learning frameworks, cannot search the whole agent design space due to the restriction of human-designed components, and thus might miss the globally optimal agent design. In this paper, we introduce Gödel Agent, a self-evolving framework inspired by the Göde…

The Mostowski Bridge
Ali Enayat
https://arxiv.org/abs/2505.23998 https://arxiv.org/pdf/2505.23998

The Mostowski Bridge
In 1950, Novak and Mostowski showed that GB (Gödel-Bernays theory of classes) is conservative over ZF, and therefore by Gödel's second incompleteness theorem the consistency of ZF is unprovable in GB. In the same year Mostowski unveiled a contrasting result: GB provides a truth-definition for ZF-formulae. Here we first give an expository account of Mostowski's construction and surrounding results, and then we show that the construction bridges the domain of Tarski-style truth theories over PA…

The idea is to provide a safe haven and a fertile ground for the next generation of scientists to work in peace and freedom to solve the most significant challenges of our time; but the geopolitical argument will prevail. As Jorge Luis Borges said in his short story “Nathaniel Hawthorne” from his book “Other Inquisitions” (1952):
“The past is indestructible; sooner or later all things return, and one of the things that return is the project to abolish the past.”

William Aspray
There was a moment in which Kurt Gödel, Albert Einstein, and John von Neumann were all roaming the halls of the Institute for Advanced Studies in Princeton at the same time. Let that information sink in. Humanity experiences such gatherings of brilliant minds in a remote location of the space-time continuum only every so often; maybe the ancient Greeks and the men of the Renaissance witnessed such periods in time, as did the IAS staff at the end of World War II. How much will we have to wait f…

This https://arxiv.org/abs/2112.12859 has been replaced.
link: https://scholar.google.com/scholar?q=a

A Countable, Dense, Dedekind-Complete Subset of $\mathbb{R}$ Constructed by Extending $\mathbb{Q}$ via Simultaneous Marking of Closed Intervals with Rational Endpoints
This article explores the model-dependent nature of set cardinality, emphasizing that cardinality is not absolute but varies across different axiomatic frameworks. Although Cantor's diagonal argument shows the real numbers are non-denumerable within ZF (Zermelo-Fraenkel set theory), the precise cardinality of the continuum remains unsettled and depends critically on model assumptions. For instance, under Gödel's inner-model axiom V=Ultimate L, the Continuum Hypothesis (CH) holds, whereas Marti…

This https://arxiv.org/abs/2505.02548 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Modal logic for reasoning about uncertainty and confusion
We consider a modal logic that can formalise statements about uncertainty and beliefs such as `I think that my wallet is in the drawer rather than elsewhere' or `I am confused whether my appointment is on Monday or Tuesday'. To do that, we expand Gödel modal logic $\mathbf{K}\mathsf{G}$ with the involutive negation $\sim$ defined as $v({\sim}ϕ,w)=1-v(ϕ,w)$. We provide semantics with the finite model property for our new logic that we call $\mathbf{K}\mathsf{G_{inv}}$ and show its equivalence…