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Math Forum » Discussions » sci.math.* » sci.math

Topic: Anti-foundation axiom
Replies: 11   Last Post: Mar 15, 2013 6:00 AM

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Zaljohar@gmail.com

Posts: 2,665
Registered: 6/29/07
Anti-foundation axiom
Posted: Mar 6, 2013 7:59 AM
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The following theory Violates foundation in preference to somewhat
plausible
axioms.

ZF - foundation
+
For all x. Exist H(x)
+
for all x. x subnumerous to H(x)
+
Anti-Foundation Axiom: An infinite Dedekindian finite set exists.

Where H(x) is the set of all sets hereditarily subnumerous to x.

Zuhair

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