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Zoekresultaten

Zoekopdracht: faculteit: "FNWI" en publicatiejaar: "2008"

AuteurRachel Sterken
TitelConcatenation as a basis for Q and the Intuitionistic variant of Nelson's Classic Result
Jaar2008
FaculteitFaculteit der Natuurwetenschappen, Wiskunde en Informatica
Instituut/afd.FNWI/FGw: Institute for Logic, Language and Computation (ILLC)
SerieILLC Master of Logic Theses / ILLC ; MoL-2008-11
SamenvattingConcatenation as a basis for Q and the Intuitionistic variant of Nelson’s Classic Result Rachel Sterken 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.
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