Pairs, sets and sequences in first-order theoriesReport as inadecuate

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Archive for Mathematical Logic

, Volume 47, Issue 4, pp 299–326

First Online: 28 June 2008Received: 30 May 2007


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.

KeywordsInterpretations Sequential theories Weak set theory Coding Mathematics Subject Classification 200003B30 03F25 03F40  Download to read the full article text

Author: Albert Visser



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