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 language | English |
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Pages (from-to) | 299-326 |
Number of pages | 28 |
Journal | Archive of Mathematical Logic |
Volume | 47 |
Issue number | 4 |
DOIs | |
Publication status | Published - 2008 |
Keywords
- Interpretations
- Sequential theories
- Weak set theory
- Coding