On the undefinability of pathological Banach spaces
Logic
2024-01-22 v1
Abstract
Motivated by Tsirelson's implicitly defined pathological Banach space, T. Gowers asked whether explicitly defined Banach spaces must include either or some . J. Iovino and P. Casazza gave an affirmative answer for first-order continuous logic. We greatly extend their work to logics with much weaker requirements than compactness on their type spaces. Noteworthy is our extensive use of the topology of function spaces (-theory) as developed by Arhangel'skii, and our use of double limit conditions studied by H. K\"onig and N. Kuhn.
Cite
@article{arxiv.2401.10459,
title = {On the undefinability of pathological Banach spaces},
author = {Clovis Hamel and Franklin D. Tall},
journal= {arXiv preprint arXiv:2401.10459},
year = {2024}
}
Comments
arXiv admin note: substantial text overlap with arXiv:2109.14513, arXiv:2004.06537