```Date: May 18, 2013 3:38 PM
Author: fom
Subject: Re: A logically motivated theory

On 5/18/2013 2:21 PM, Zuhair wrote:> On May 18, 8:58 pm, fom <fomJ...@nyms.net> wrote:>> On 5/18/2013 10:40 AM, Zuhair wrote:>>>>> In this theory Sets are nothing but object extensions of some>>> predicate. This theory propose that for every first order predicate>>> there is an object extending it defined after some extensional>>> relation.>>>>> This goes in the following manner:>>>>> Define: E is extensional iff for all x,y: (for all z. z E x iff z E y)>>> -> x=y>>>>> where E is a primitive binary relation symbol.>>>> So,>>>> <X,E>>>>> is a model of the axiom of extensionality.>>>>> Now sets are defined as>>>>> x is a set iff Exist E,P: E is extensional & for all y. y E x <-> P(y)>>>> So,>>>> xEX <-> ...>>>> where>>>> ... is a statement quantifying over relations and predicates.>> No ... is a statement quantifying over objects.>>How so?  The formula seems to have anexistential quantifier applying to arelation and a subformula with thequantified 'E' as a free variable:'E is extensional'Using 'R' for "Relation", I readAx(Set(x) <-> EREP(extensional(R) /\ Ay(yRx <-> P(y))))
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