Cumulative Higher-Order Logic as a Foundation for Set Theory

Cumulative Higher-Order Logic as a Foundation for Set Theory

Cached

Download Links

[ftp.tcs.informatik.uni-muenchen.de]
[math.ucsd.edu]

Other Repositories/Bibliography

DBLP

by Wolfgang Degen , Jan Johannsen

Citations:

1 - 1 self

Versions

Version History

Metadata Version 2

User correction supplied by SystemCorrections

Datum	Value	Source
TITLE	Cumulative Higher-Order Logic as a Foundation for Set Theory	user correction - Legacy Corrections
AUTHOR NAME	Wolfgang Degen	user correction - Legacy Corrections
AUTHOR AFFIL	; 1; 2; Institut fur Informatik, Ludwig-Maximilians-Universitat Munchen	user correction - Legacy Corrections
AUTHOR ADDR	; IMMD 1, Universitat Erlangen-Nurnberg, Germany	user correction - Legacy Corrections
AUTHOR NAME	Jan Johannsen	user correction - Legacy Corrections
ABSTRACT	The systems K of transnite cumulative types up to are extended to systems K 1 that include a natural innitary inference rule, the so-called limit rule. For countable a semantic completeness theorem for K 1 is proved by the method of reduction trees, and it is shown that every model of K 1 is equivalent to a cumulative hierarchy of sets. This is used to show that several axiomatic rst-order set theories can be interpreted in K 1 , for suitable . Keywords: cumulative types, innitary inference rule, logical foundations of set theory. MSC: 03B15 03B30 03E30 03F25 1 Introduction The idea of founding mathematics on a theory of types was rst proposed by Russell [20] (foreshadowed already in [19]), and subsequently implemented by Whitehead and Russell [26]. The formal systems presented in these works were later simplied and cast into their modern shape by Ramsey [18]. Godel [9] and Tarski [25] were the rst to restrict the type structure to types of unary predi...	user correction - Legacy Corrections
PAGES	147--170	INFERENCE
VOLUME	46	INFERENCE
CITATIONS	25 found	ParsCit 1.0