Pairs, Sets and Sequences in First Order Theories

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Abstract

In this paper we study the idea of theories with containers, like sets, pairs, sequences. We provide a modest framework to study such theories. We prove two concrete results. First, we show that first-order theories of finite signature that have functional non-surjective ordered pairing are definitionally equivalent to extensions in the same language of the basic theory of non-surjective ordered pairing. Second, we show that a first-order theory of finite signature is sequential (is a theory of sequences) iff it is definitionally equivalent to an extension in the same language of a system of weak set theory called WS.
Original languageEnglish
Pages (from-to)299-326
Number of pages28
JournalArchive of Mathematical Logic
Volume47
Issue number4
DOIs
Publication statusPublished - 2008

Keywords

  • Interpretations
  • Sequential theories
  • Weak set theory
  • Coding

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