Weak Monadic Second Order Theory of Successor is not Element-recurive
Name
MIT-LCS-TM-038.pdf
Size
920.34 KB
Format
Adobe PDF
Checksum (MD5)
fe3c9eedcc24567158a939b252a5ce57
Author(s)
Meyer, Albert R.
Date Issued
December 1973
Series/Report no.
MIT-LCS-TM-038
MAC-TM-038
Abstract
Let L SIS be the set of formulas expressible in a week monadic second order logic using only the predicates [x =y+1] and [x E z]. Bucci and Elgot [3,4] have shown that the truth of sentences in L SIS (under the standard interpretation < N, successor > with second order variables interpreted as ranging over finite sets) is decidable. We refer to the true sentences in L SIS as WSIS. We shall prove that WSIS is not elementary-recursive in the sense of Kalmar. In fact, we claim a stronger result:
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