DE JONGH

Logic
PROVABILITY AND INTERPRETABILITY LOGIC

Workshop

DICK DE JONGH

ILLC: WINS, University of Amsterdam

Second week
dickdj@wins.uva.nl

Course description

Since the seventies modal logic, especially the modal logic GL, has been applied to study properties of the formalized provability predicate of (arithmetical) theories. Arithmetic completeness of GL for propositional reasoning about provability (which greatly strengthens Goedel's second incompleteness theorem) was proved by Solovay for arithmetic realizations in Peano, and fixed point theorems were established for GL. Since that time the main achievements have been to show that similar results mostly fail for predicate logic, to recognize reasoning about more complex notions like interpretability where arithmetic can be shown to reason adequately, and also to strengthen Solovay's results directly. The area has implications for proof theory, (bounded/intuitionistic) arithmetic as well as for modal logic.

The aim of the workshop is to bring together researchers with a direct or indirect (arithmetical, proof-theoretical, or modal-logical) interest in the subject.

Prerequsites
None

Literature
No specific recommendation

HOME PROGRAMME CONTACT REGISTRATION

Logic	PROVABILITY AND INTERPRETABILITY LOGIC
Workshop	DICK DE JONGH ILLC: WINS, University of Amsterdam
Second week	dickdj@wins.uva.nl
Course description	Since the seventies modal logic, especially the modal logic GL, has been applied to study properties of the formalized provability predicate of (arithmetical) theories. Arithmetic completeness of GL for propositional reasoning about provability (which greatly strengthens Goedel's second incompleteness theorem) was proved by Solovay for arithmetic realizations in Peano, and fixed point theorems were established for GL. Since that time the main achievements have been to show that similar results mostly fail for predicate logic, to recognize reasoning about more complex notions like interpretability where arithmetic can be shown to reason adequately, and also to strengthen Solovay's results directly. The area has implications for proof theory, (bounded/intuitionistic) arithmetic as well as for modal logic. The aim of the workshop is to bring together researchers with a direct or indirect (arithmetical, proof-theoretical, or modal-logical) interest in the subject.
Prerequsites	None
Literature	No specific recommendation