Geodesic
Separation Principles and Bounded Quantification
Canadian mathematical bulletin, Tome 18 (1975) no. 2, pp. 295-296

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This note is concerned with the implication SepII (Q)→SepI (Q) where Q is a class of subsets of some set S. where cZ denotes S—Z.It is well-known that in general the above implication is false (e.g. let Q be the closed subsets of the reals). 
Dawes, A. M. Separation Principles and Bounded Quantification. Canadian mathematical bulletin, Tome 18 (1975) no. 2, pp. 295-296. doi: 10.4153/CMB-1975-056-4
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[1] 1. Addison, J. W., Separation principles in the hierarchies of classical and effective descriptive set theory. Fundamenta Mathematicae XLVI (1958) pp. 123-135. Google Scholar

[2] 2. Dawes, A. M., First-order hierarchies in general models and in models of Peano arithmetic. Ph.D. thesis, University of Toronto, Toronto, 1972. Google Scholar

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