Add to ORKGWe study the structure of families of theories in the language of arithmetic extended to allow these families to refer to one another and to themselves. If a theory contains schemata expressing its own truth and expressing a specific Turing index for itself, and contains some other mild axioms, then that theory is untrue. We exhibit some families of true self-referential theories that barely avoid this forbidden pattern
I develop some of the theory of self-referential systems. I present the necessary semantic ideas, an...
In this thesis, we investigate the semantics of systems which can refer to themselves, e.g., by ``pa...
Typical arguments for results like Kleene's Second Recursion Theorem and theexistence of self-writin...
We study the structure of families of theories in the language of arithmetic extended to allow these...
In this paper we examine various requirements on the formalisation choices under which self-referenc...
Self-reference has played a prominent role in the development of metamathematics in the past century...
We consider an extension of first-order logic with a recursion operator that corresponds to allowing...
The G ödelian Arguments represent the effort done to interpret Gödel's Incompleteness Theorems in o...
The consistency formula for set theory T e. g. Zermelo-Fraenkel set theory ZF, can be stated in form...
I put forward precise and appealing notions of reference, self-reference, and well-foundedness for s...
The aim of this paper is to provide a minimalist axiomatic theory of truth based on the notion of re...
In this sequel to Self-reference in arithmetic I we continue our discussion of the question: What do...
A Gödel sentence is often described as a sentence saying about itself that it is not provable and a ...
A Gödel sentence is often described as a sentence saying about itself that it is not provable, and a...
In this paper we prove the consistency of a variant of Church's Thesis than can be formulated as a s...
I develop some of the theory of self-referential systems. I present the necessary semantic ideas, an...
In this thesis, we investigate the semantics of systems which can refer to themselves, e.g., by ``pa...
Typical arguments for results like Kleene's Second Recursion Theorem and theexistence of self-writin...
We study the structure of families of theories in the language of arithmetic extended to allow these...
In this paper we examine various requirements on the formalisation choices under which self-referenc...
Self-reference has played a prominent role in the development of metamathematics in the past century...
We consider an extension of first-order logic with a recursion operator that corresponds to allowing...
The G ödelian Arguments represent the effort done to interpret Gödel's Incompleteness Theorems in o...
The consistency formula for set theory T e. g. Zermelo-Fraenkel set theory ZF, can be stated in form...
I put forward precise and appealing notions of reference, self-reference, and well-foundedness for s...
The aim of this paper is to provide a minimalist axiomatic theory of truth based on the notion of re...
In this sequel to Self-reference in arithmetic I we continue our discussion of the question: What do...
A Gödel sentence is often described as a sentence saying about itself that it is not provable and a ...
A Gödel sentence is often described as a sentence saying about itself that it is not provable, and a...
In this paper we prove the consistency of a variant of Church's Thesis than can be formulated as a s...
I develop some of the theory of self-referential systems. I present the necessary semantic ideas, an...
In this thesis, we investigate the semantics of systems which can refer to themselves, e.g., by ``pa...
Typical arguments for results like Kleene's Second Recursion Theorem and theexistence of self-writin...