On Equivalents of Well-foundedness -- An experiment in Mizar

On Equivalents of Well-foundedness -- An experiment in Mizar (1998)

by Piotr Rudnicki , Andrzej Trybulec

Citations:

11 - 3 self

User correction supplied by mph

Datum	Value	Source
TITLE	On Equivalents of Well-foundedness -- An experiment in Mizar	user correction
AUTHOR NAME	Piotr Rudnicki	user correction
AUTHOR AFFIL	Contents	user correction
AUTHOR ADDR	Canada	user correction
AUTHOR NAME	Andrzej Trybulec	user correction
AUTHOR AFFIL	Contents	user correction
ABSTRACT	Four statements equivalent to well-foundedness (well-founded induction, existence of recursively defined functions, uniqueness of recursively defined functions, and absence of descending omega-chains) have been proved in Mizar and the proofs mechanically checked for correctness. It seems not to be widely known that the existence (without the uniqueness assumption) of recursively defined functions implies well-foundedness. In the proof we used regular cardinals, a fairly advanced notion of set theory. The theory of cardinals in Mizar was developed earlier by G. Bancerek. With the current state of the Mizar system, the proofs turned out to be an exercise with only minor additions at the fundamental level. We would like to stress the importance of a systematic development of a mechanized data base for mathematics in the spirit of the QED Project.	user correction - Legacy Corrections
YEAR	1998	user correction
CITATIONS	51 found	ParsCit 1.0