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RTA
2007
Springer
15 years 3 months ago
A Simple Proof That Super-Consistency Implies Cut Elimination
Abstract. We give a simple and direct proof that super-consistency implies cut elimination in deduction modulo. This proof can be seen as a simplification of the proof that super-...
Gilles Dowek, Olivier Hermant
66
Voted
CADE
2006
Springer
15 years 9 months ago
Combining Type Theory and Untyped Set Theory
Abstract. We describe a second-order type theory with proof irrelevance. Within this framework, we give a representation of a form of Mac Lane set theory and discuss automated supp...
Chad E. Brown
JAR
2007
123views more  JAR 2007»
14 years 9 months ago
Reasoning about Object-based Calculi in (Co)Inductive Type Theory and the Theory of Contexts
Abstract. We illustrate a methodology for formalizing and reasoning about Abadi and Cardelli’s object-based calculi, in (co)inductive type theory, such as the Calculus of (Co)Ind...
Alberto Ciaffaglione, Luigi Liquori, Marino Micula...
73
Voted
CORR
2002
Springer
67views Education» more  CORR 2002»
14 years 9 months ago
The prospects for mathematical logic in the twenty-first century
Abstract. The four authors present their speculations about the future developments of mathematical logic in the twenty-first century. The areas of recursion theory, proof theory a...
Samuel R. Buss, Alexander S. Kechris, Anand Pillay...
BSL
2004
100views more  BSL 2004»
14 years 9 months ago
Forcing in proof theory
Paul Cohen's method of forcing, together with Saul Kripke's related semantics for modal and intuitionistic logic, has had profound effects on a number of branches of mat...
Jeremy Avigad