0100496316

open access

Accepted Manuscript

Smullyan’s truth and provability

English (英語)

Journal of Logic and Computation

35(5)

exaf001

Oxford University Press (OUP)

2025-07

2026-01-20

Published Online: 2025-01-20

We revisit Smullyan’s paper ‘Truth and Provability’ (2013) for three purposes. First, we introduce the notion of Smullyan models to give a precise definition for Smullyan’s framework discussed in that paper. Second, we clarify the relationship between three theorems proved by Smullyan and other newly introduced properties for Smullyan models in terms of both implications and non-implications. Third, we construct two Smullyan models based on arithmetical ideas and show the correspondence between the properties of these Smullyan models and those concerning truth and provability in arithmetic.

学術雑誌論文

This is a pre-copyedited, author-produced version of an article accepted for publication in [Journal of Logic and Computation] following peer review. The version of record [Taishi Kurahashi, Kohei Tominaga, Smullyan’s truth and provability, Journal of Logic and Computation, Volume 35, Issue 5, July 2025, exaf001] is available online at: https://doi.org/10.1093/logcom/exaf001