MoL-2008-11: Concatenation as a basis for Q and the Intuitionistic variant of Nelson's Classic Result

MoL-2008-11: Sterken, Rachel (2008) Concatenation as a basis for Q and the Intuitionistic variant of Nelson's Classic Result. [Report]

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Abstract

Visser shows that a first-order theory is sequential (has ‘global coding’) iff (roughly) it directly interprets a weak set theory, AS. The programme behind Visser’s result is to find coordinate free ways of thinking about notions of coding. In this thesis, we add some results to Visser’s programme for the case of ‘local coding’. Since Robinson’s arithmetic, Q, is mutually interpretable (but not directly) with AS and Q is in a sense the minimal arithmetical theory that yields enough coding to prove G¨odel’s Second Incompleteness Theorem, we propose whether a theory interprets Q as a characterization of the notion of ‘local coding’. We also investigate other candidates in place of Q. We show that a basic theory of strings, TC_Q interprets Q. We, in addition, verify that the classical result of Nelson works in the constructive case by showing that iQ interprets iI\Delta_0+\Omega_1. This result entails that our characterization of ‘local coding’ also works in the constructive case.

Item Type: Report
Report Nr: MoL-2008-11
Series Name: Master of Logic Thesis (MoL) Series
Year: 2008
Date Deposited: 12 Oct 2016 14:38
Last Modified: 12 Oct 2016 14:38
URI: https://eprints.illc.uva.nl/id/eprint/806

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