A finite axiomatization of inductive-recursive definitions

A finite axiomatization of inductive-recursive definitions (1999)

by Peter Dybjer , Anton Setzer

Venue:	Typed Lambda Calculi and Applications, volume 1581 of Lecture Notes in Computer Science
Citations:	35 - 11 self

Datum	Value	Source
TITLE	A finite axiomatization of inductive-recursive definitions	INFERENCE
AUTHOR NAME	Peter Dybjer	SVM HeaderParse 0.2
AUTHOR NAME	Anton Setzer	SVM HeaderParse 0.2
ABSTRACT	Induction-recursion is a schema which formalizes the principles for introducing new sets in Martin-Löf’s type theory. It states that we may inductively define a set while simultaneously defining a function from this set into an arbitrary type by structural recursion. This extends the notion of an inductively defined set substantially and allows us to introduce universes and higher order universes (but not a Mahlo universe). In this article we give a finite axiomatization of inductive-recursive definitions. We prove consistency by constructing a set-theoretic model which makes use of one Mahlo cardinal. 1	SVM HeaderParse 0.2
YEAR	1999	INFERENCE
VENUE	Typed Lambda Calculi and Applications, volume 1581 of Lecture Notes in Computer Science	INFERENCE
VENUE TYPE	CONFERENCE	INFERENCE
PAGES	129--146	INFERENCE
CITATIONS	25 found	ParsCit 1.0