17 citations · 23 across the 5 of their papers we have counts for
9 papers · 1 filter
Finitely Axiomatized Theories Lack Self-Comprehension
Fedor Pakhomov, Albert Visser
In this paper we prove that no consistent finitely axiomatized theory one-dimensionally interprets its own extension with predicative comprehension. This constitutes a result with…
Cyclic Henkin Logic
Albert Visser
In this paper, we study Cyclic Henkin Logic CHL, a logic that can be described as provability logic without the third Löb condition, to wit, that provable implies provably provable…
Self-reference Upfront: A Study of Self-referential Gödel Numberings
Balthasar Grabmayr, Albert Visser
In this paper we examine various requirements on the formalisation choices under which self-reference can be adequately formalised in arithmetic. In particular, we study self-refer…
The interpretability logic of all reasonable arithmetical theories
Joost J. Joosten, Albert Visser
This paper from 2000 is a presentation of a status quæstionis at that tiime, to wit of the problem of the interpretability logic of {\em all}\/ reasonable arithmetical theories. We…
Enayat Theories
Albert Visser
In this paper we study solution attempts for a problem posed by Ali Enayat: can there be a finitely axiomatized consistent sequential theory that interprets itself plus the (senten…
The Small-Is-Very-Small Principle
Albert Visser
The central result of this paper is the small-is-very-small principle for restricted sequential theories. The principle says roughly that whenever the given theory shows that a pro…