# MULTIDIMENSIONAL EXACT CLASSES, SMOOTH APPROXIMATION AND BOUNDED 4-TYPES

@article{Wolf2020MULTIDIMENSIONALEC,
title={MULTIDIMENSIONAL EXACT CLASSES, SMOOTH APPROXIMATION AND BOUNDED 4-TYPES},
author={D. Wolf},
journal={The Journal of Symbolic Logic},
year={2020},
volume={85},
pages={1305 - 1341}
}
• D. Wolf
• Published 2020
• Computer Science, Mathematics
• The Journal of Symbolic Logic
Abstract In connection with the work of Anscombe, Macpherson, Steinhorn and the present author in [1] we investigate the notion of a multidimensional exact class (R-mec), a special kind of multidimensional asymptotic class (R-mac) with measuring functions that yield the exact sizes of definable sets, not just approximations. We use results about smooth approximation [24] and Lie coordinatization [13] to prove the following result (Theorem 4.6.4), as conjectured by Macpherson: For any countable… Expand

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