Abstract
As emphazised in the introduction, a DP is slightly more than a crib for a lazy mathematician to prove his theorems. Indeed, if the system is not wholly trivial, in most cases it is much too difficult to carry-through a DP. The usefulness of a DP is to be found rather in the information about the system in question obtained from the DP. So we have got in chapter I a complete axiom system for SC consulting the DP. In this chapter we will use the DP to answer questions concerning the strength of SC: What relations on natural numbers are expressible in SC? And what about relations on sets of natural numbers? In other words: To which part of the whole number theory does SC correspond? This question is answered best by comparing SC with other number theoretic systems, and by asking for the there definable sets and relations.
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© 1970 Springer-Verlag Berlin Heidelberg
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Siefkes, D. (1970). Benefits of the decision procedure. In: Büchi’s Monadic Second Order Successor Arithmetic. Lecture Notes in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-36678-3_2
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DOI: https://doi.org/10.1007/978-3-662-36678-3_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-35848-1
Online ISBN: 978-3-662-36678-3
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