Pairs,sets and sequences in first-order theories |
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Authors: | Albert Visser |
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Institution: | (1) Department of Philosophy, Faculty of Humanities, Utrecht University, Heidelberglaan 8, 3584 CS Utrecht, The Netherlands |
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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.
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Keywords: | Interpretations Sequential theories Weak set theory Coding |
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