[FOM] Set Theories without the extensionality axiom

jbell@uwo.ca jbell at uwo.ca
Thu Jul 9 12:23:20 EDT 2009


A system of (constructive) set theory without the axiom of extensionality is 
investigated in my paper 'The Axiom of Choice and the Law of Excluded Middle 
in Weak Set Theories", Mathematical Logic Quarterly, 54, no. 2, 2008. It may 
also be accessed on my website.

John Bell
Professor John L. Bell
Department of Philosophy
University of Western Ontario
London, Ontario N6A 3K7
Canada

http://publish.uwo.ca/%7Ejbell/



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Subject: FOM Digest, Vol 79, Issue 2


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>   1. 5th Conference on Logic, Computability and Randomness
>      (Joseph S. Miller)
>   2. Set theories without the extensionality axiom (ioachim drugus)
>   3. [CiE] CiE 2009 in Heidelberg - Final Call for Participation (CiE)
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> Message: 1
> Date: Wed, 8 Jul 2009 10:58:22 +0200
> From: "Joseph S. Miller" <joseph.s.miller at gmail.com>
> Subject: [FOM] 5th Conference on Logic, Computability and Randomness
> To: kolmogorov at idsia.ch, fom at cs.nyu.edu
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> [Posted for Peter Cholak]
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> Please forward to this?announcement to everyone who might be
> interested. Sorry about the?multiple copies.
> ________________
>
> The 5th Conference on Logic, Computability and Randomness will be held
> at Notre Dame May 24-28, 2010.? The arrival day is May 23. ?The
> meeting will end by 1pm on the 28th. The meeting? URL is
>
> http://math.nd.edu/conferences/AlgoRandomness/
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> Please save the dates.? More info about the meeting will be available
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> This meeting is supported by the?National Science Foundation via
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> -Peter
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>
> ------------------------------
>
> Message: 2
> Date: Wed, 8 Jul 2009 02:42:20 -0700 (PDT)
> From: ioachim drugus <ioachim.drugus at yahoo.com>
> Subject: [FOM] Set theories without the extensionality axiom
> To: fom at cs.nyu.edu
> Message-ID: <783138.75999.qm at web55804.mail.re3.yahoo.com>
> Content-Type: text/plain; charset=us-ascii
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>
>
> Greetings!
>
> I would appreciate if somebody can help me find any reference to an 
> axiomatic set theory without the extensionality axiom.
> Here are merits of such a set theory:
> 1. This would be a set theory with "multiple universes of discourse", 
> where the "unlimited"
> set abstraction {x :F(x)} could be treated as the set abstraction {x in U 
> : F(x)}, limited by a universe of discourse on which we are focused (as 
> many authors,  I am using the reserved word "in" as a denotation of the 
> membership relationship in plain text).
> 2. The entities studied by such a theory would be multi-identity. This 
> would be a theory of multi-sets, where the modifier "multi-" refers not 
> only to the elements of a set which may encounter in many copies 
> (replicas), but also to the set itself - it is allowed to also be present 
> in many copies. Also, the modifier "multi-" applies to the atoms 
> (urelements) - they can also be present in multiple copies.
>
> Thank you,
> Ioachim Drugus,
> Main Software Architect,
> SemanticSoft, Inc.
>
>
>
>
>
>
>
> ------------------------------
>
> Message: 3
> Date: Wed, 08 Jul 2009 10:05:11 -0700
> From: CiE <cie at maths.leeds.ac.uk> (by way of Martin Davis
> <martin at eipye.com>)
> Subject: [FOM] [CiE] CiE 2009 in Heidelberg - Final Call for
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