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We prove that it is not possible to define an appropriate notion of rank in set theories without the axiom of foundation.
A lattice-valued set theory is formulated by introducing the logical implication
which represents the order relation on the lattice.
Let d be a Turing degree containing differences of recursively enumerable sets (d.r.e.sets) and R[d] be the class of less than d r.e. degrees in whichd is relatively enumerable (r.e.). A.H.Lachlan proved that for any non-recursive d.r.e. d
R[d] is not empty. We show that the r.e. degree defined...
Given a simple non-trivial finite-dimensional Lie algebra L, fields
and Chevalley groups
, we first prove that
is isomorphic to
. Then we consider the case of Chevalley groups of twisted type
. We obtain a...
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