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- W2134972382 abstract "We study projective subsets of Baire space from Brouwer's intuitionistic point of view, using his Thesis on Bars and his continuity axioms. We first study analytic sets; these are the projections of the closed subsets of Baire space. We consider a number of examples and discover a fine structure in the class of the analytic sets that fail to be positively Borel. A subset of Baire space is strictly analytic if it coincides with the range of a continuous function from Baire space to itself. We prove separation and boundedness theorems for strictly analytic sets. Co-analytic sets are the co-projections of the open subsets of Baire space. We show different ways to prove that some co-analytic sets are not analytic and that some analytic sets are not co-analytic. We consider the set of the codes of the closed and located subsets of Baire space that are almost-countable as an example of a set that is a projection of a co-analytic set. We bring to light the collapse of the projective hierarchy: every (positively) projective set coincides with the projection of a co-analytic set." @default.
- W2134972382 created "2016-06-24" @default.
- W2134972382 creator A5084987525 @default.
- W2134972382 date "2011-04-15" @default.
- W2134972382 modified "2023-09-27" @default.
- W2134972382 title "Analytic, co-analytic and projective sets from Brouwer's intuitionistic perspective" @default.
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