[FOM] Disguised Set Theory "DST"

Zuhair Abdul Ghafoor Al-Johar zaljohar at yahoo.com
Sat Oct 1 15:05:52 EDT 2011

Dear FOMers.

DST is a theory that I defined in first order logic with equality "=" and
membership "e". The theory has a scheme that looks paradoxical at first 
glance but proves to be quite evasive. The theory can interpret bounded
ZF-Power-Infinity; can define big sets that ZF can't. However the
consistency of this theory remains an open question.

The theory is actually very simple. It's an extensional pure set theory,
every set has a transitive closure "TC" defined as the minimal transitive
superset, induction for transitive closures is stipulated. A binary
membership relation E is defined as:

x E y iff (x e y and not y e TC(x))

The comprehension scheme simply states that for every formula phi using
only predicates = and E, the set {x|phi} exists.

See: http://zaljohar.tripod.com/dst.pdf



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