0AppA071110 - 1 APPENDIX A PRINCIPAL CLASSES OF FUNCTIONS...

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1 APPENDIX A PRINCIPAL CLASSES OF FUNCTIONS AND SETS N is the set of all nonnegative integers. |x| is max(x). MF is the set of all functions whose domain is a subset of some N k and whose range is a subset of N. SD is the set of all f MF such that for all x dom(f), f(x) > |x|. EVSD is the set of all f MF such that for all but finitely many x dom(f), f(x) > |x|. ELG is the set of all f MF such that there exist c,d > 1 obeying the following condition. For all but finitely many x dom(f), c|x| f(x) d|x|. LB is the set of all f MF such that there exists d obeying the following condition. For all x dom(f), |x| d|x|. EXPN is the set of all f MF such that there exists c > 1 obeying the following condition. For all but finitely many x dom(f), c|x| f(x). BAF is the set of all f MF which can be written using 0,1,+,-,•, ,log, where x-y = max(x-y,0), x = 2 x , log(x) = floor(log(x)) if x > 0; 0 otherwise. Closure under definition by cases, using <,=, is derived in section 5.1. INF is the set of all infinite subsets of N.
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0AppA071110 - 1 APPENDIX A PRINCIPAL CLASSES OF FUNCTIONS...

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