A New Approach to Predicative Set Theory
Graduate studies at Western
|Abstract||We suggest a new framework for the Weyl-Feferman predicativist program by constructing a formal predicative set theory P ZF which resembles ZF , and is suitable for mechanization. The basic idea is that the predicatively acceptable instances of the comprehension schema are those which determine the collections they deﬁne in an absolute way, independent of the extension of the “surrounding universe”. The language of P ZF is type-free, and it reﬂects real mathematical practice in making an extensive use of statically deﬁned abstract set terms. Another important feature of P ZF is that its underlying logic is ancestral logic (i.e. the extension of ﬁrst-order logic with a transitive closure operation)|
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
|External links||This entry has no external links. Add one.|
|Through your library||Only published papers are available at libraries|
Similar books and articles
Fernando Ferreira (1999). A Note on Finiteness in the Predicative Foundations of Arithmetic. Journal of Philosophical Logic 28 (2):165-174.
P. T. Johnstone (1987). Notes on Logic and Set Theory. Cambridge University Press.
Johannes Heidema (1990). An Axiom Schema of Comprehension of Zermelo–Fraenkel–Skolem Set Theory. History and Philosophy of Logic 11 (1):59-65.
Solomon Feferman & Geoffrey Hellman (1995). Predicative Foundations of Arithmetic. Journal of Philosophical Logic 24 (1):1 - 17.
Ralf-Dieter Schindler (1993). Prädikative Klassen. Erkenntnis 39 (2):209 - 241.
M. Randall Holmes (1995). The Equivalence of NF-Style Set Theories with "Tangled" Theories; the Construction of Ω-Models of Predicative NF (and More). Journal of Symbolic Logic 60 (1):178-190.
Paul Strauss (1991). Arithmetical Set Theory. Studia Logica 50 (2):343 - 350.
Added to index2009-04-13
Total downloads8 ( #131,909 of 739,053 )
Recent downloads (6 months)0
How can I increase my downloads?