Skip to main content

Benefits of the decision procedure

  • Chapter
  • 302 Accesses

Part of the Lecture Notes in Mathematics book series (LNM)

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.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   49.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and Permissions

Copyright information

© 1970 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

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

Download citation

  • 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

  • eBook Packages: Springer Book Archive