Higher set theory

Abstract

Russell’s way out of his paradox via the impre-dicative theory of types has roughly the same logical power as Zermelo set theory - which supplanted it as a far more flexible and workable axiomatic foundation for mathematics. We discuss some new formalisms that are conceptually close to Russell, yet simpler, and have the same logical power as higher set theory - as represented by the far more powerful Zermelo-Frankel set theory and beyond. END.

Categories

Keywords

Reprint years

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,386

External links

  • This entry has no external links. Add one.
Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

  • Only published works are available at libraries.

My notes

Similar books and articles

Hilberts Logik. Von der Axiomatik zur Beweistheorie.Volker Peckhaus - 1995 - NTM Zeitschrift für Geschichte der Wissenschaften, Technik und Medizin 3 (1):65-86.
The origins of zermelo's axiomatization of set theory.Gregory H. Moore - 1978 - Journal of Philosophical Logic 7 (1):307 - 329.
From Traditional Set Theory – that of Cantor, Hilbert , Gödel, Cohen – to Its Necessary Quantum Extension.Edward G. Belaga - manuscript
Axiomatization of set theory by extensionality, separation, and reducibility.Harvey Friedman - manuscript
Beyond first-order logic: the historical interplay between mathematical logic and axiomatic set theory.Gregory H. Moore - 1980 - History and Philosophy of Logic 1 (1-2):95-137.
The inconsistency of higher order extensions of Martin-löf's type theory.Bart Jacobs - 1989 - Journal of Philosophical Logic 18 (4):399 - 422.
Concept calculus: Much better than.Harvey M. Friedman - unknown
Is any set theory true?Joseph S. Ullian - 1969 - Philosophy of Science 36 (3):271-279.
Higher Order Modal Logic.Reinhard Muskens - 2006 - In Patrick Blackburn, Johan Van Benthem & Frank Wolter (eds.), Handbook of Modal Logic. Elsevier. pp. 621-653.
From Russell's paradox to.Harvey M. Friedman - unknown

Analytics

Added to PP
2009-01-28

Downloads
85 (#194,716)

6 months
1 (#1,510,037)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Intermediate Logics and the de Jongh property.Dick de Jongh, Rineke Verbrugge & Albert Visser - 2011 - Archive for Mathematical Logic 50 (1-2):197-213.
Platonistic formalism.L. Horsten - 2001 - Erkenntnis 54 (2):173-194.

Add more citations

References found in this work

No references found.

Add more references