Abstract:The purpose of this paper is to show that arithmetically minimal systems of notations can be constructed which provide notations for all ramified analytical ordinals (all the ordinals in the minimum β-model for analysis). This is a much larger section of the second number class than the Church-Kleene constructive ordinals (although still only an initial segment of the ordinals). Arithmetic minimality means that if H is an “H-set” associated with an ordinal α in our system and H′ is an H-set associated with th… Show more
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