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For the classA of uncountable Archimedian real closed fields we show that the statement “TheL
<ω-theory ofA is complete” is independent of ZFC. In particular we have the following results:
From the hypothesis that all Turing closed games are determined we prove: (1) the Continuum Hypothesis and (2) every subset of ℵ1 is constructible from a real.
Investigating Girard's new propositionnal calculus which aims at a large scale study of computation, we stumble quickly on that question: What is a multiplicative connective? We give here a detailed answer together with our motivations and expectations.
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