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math.LO2025
An axiomatization of truth and paradoxicality
Luca Castaldo
This short note introduces a formal system of truth and paradoxicality, outlining the main motivation, and proving its -consistency. The system is called TP, for 'Truth and Para…
math.LO2024
On Classical Determinate Truth
Luca Castaldo, Carlo Nicolai
The paper proposes and studies new classical, type-free theories of truth and determinateness with unprecedented features. The theories are fully compositional, strongly classical…
math.LO2020★ 1 cited
KF, PKF, and Reinhardt's Program
Luca Castaldo, Johannes Stern
In 'Some Remarks on Extending an Interpreting Theories with a Partial Truth Predicate' Reinhardt famously proposed an instrumentalist interpretation of the truth theory Kripke-Fefe…