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Quantifier Rank Spectrum of L, (PhD Thesis Defense)
 

Summary: Quantifier Rank Spectrum of
L, (PhD Thesis Defense)
by Nathanael Leedom Ackerman
April 19, 2006
Definition 1. If L is a relational language then
L1,(L) is the smallest collection of formulas
such that if (x) L1,(L) then
L L1,(L)
(x) L1,(L)
(y)(x) L1,(L)
(y)(x) L1,(L)
and if {i(x) : i } L1,(L) where iFree
Variables(i) is finite then
i i(x) L1,(L)
i i(x) L1,(L)
1
Definition 2. If L is a relational language and
(x) L1,(L) we define the quantifier rank
of (x) (qr((x))) by induction:
qr(R(x)) = 0 if R is a relation in L.

  

Source: Ackerman, Nate - Department of Mathematics, University of Pennsylvania

 

Collections: Mathematics