A Framework for Formalizing Set Theories Based on the Use of Static Set Terms


Authors
Arnon Avron
Tel Aviv University
Abstract
We present a new unified framework for formalizations of axiomatic set theories of different strength, from rudimentary set theory to full ZF . It allows the use of set terms, but provides a static check of their validity. Like the inconsistent “ideal calculus” for set theory, it is essentially based on just two set-theoretical principles: extensionality and comprehension (to which we add ∈-induction and optionally the axiom of choice). Comprehension is formulated as: x ∈ {x | ϕ} ↔ ϕ, where {x | ϕ} is a legal set term of the theory. In order for {x | ϕ} to be legal, ϕ should be safe with respect to {x}, where safety is a relation between..
Keywords No keywords specified (fix it)
Categories No categories specified
(categorize this paper)
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 51,480
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

No references found.

Add more references

Citations of this work BETA

The Middle Ground-Ancestral Logic.Liron Cohen & Arnon Avron - 2019 - Synthese 196 (7):2671-2693.

Add more citations

Similar books and articles

Analytics

Added to PP index
2009-01-28

Total views
5 ( #1,097,808 of 2,330,851 )

Recent downloads (6 months)
1 ( #587,623 of 2,330,851 )

How can I increase my downloads?

Downloads

My notes