[FOM] non-extensional models of set theory

[Alasdair Urquhart]

Robin Gandy published two papers on the axiom of extensionality in the
JSL.

 	On the Axiom of Extensionality Part 1: JSL Vol. 21 (1956), pp. 36-48

This proves the consistency of TT+Ext relative to TT, where TT is
the simple theory of types.

 	On the Axiom of Extensionality Part 2: JSL Vol. 24 (1959), pp. 287-300.

This proves the consistency of GB+Ext relative to GB, where GB is
Goedel-Bernays set theory.



On Wed, 1 Apr 2015, william tait wrote:

> Robbin Gandy had a paper on that in the 1950's in JSL. I think it is the result you have in mind.
>
> Bill
>
> Sent from my iPad
>
>> On Apr 1, 2015, at 10:18 AM, Paul B Levy <P.B.Levy at cs.bham.ac.uk> wrote:
>>
>>
>> Dear all,
>>
>> Is there a result in the literature along the following lines?
>>
>> Given a model of ZF without Extensionality, its "extensional quotient" is a model of ZF including Extensionality.
>>
>> Paul
>>
>>
>>
>> --
>> Paul Blain Levy
>> School of Computer Science, University of Birmingham
>> http://www.cs.bham.ac.uk/~pbl
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