On the Use of Inaccessible Numbers and Order Indiscernibles in Lower Bound Arguments for Random Access Machines

and DISJOINT SETS:: {(yr,. ",!n¡2,2r,"',zntz) e N" I n is even and {Y""' '!n¡z\ ^ {2""''z'¡'\: Ø} on random access machines where the number of registers is bounded by an arbitrary function of n. nontrivial (i.e', superlinear) optimal lower bound on the computa problem on a random acc€ss machine' We will also show that (n log n) is relatively stable insofar"as it remains valid if we attach an arbitrary oracle 0 ç Nt to the RAM, which may be queried about arbitrary q-tuples of input numbers (4 is an arbitrary constant)' Applications of our l,ower bound arguments to other problems will be discussed in Remark 2.5.