PreprintarXiv licencearXiv
A characterization of the finite model property for ω-categorical theories
Abstract
A first-order theory T has the {\em finite model property} if every first-order sentence that is implied by T has a finite model. We give a characterization of when a complete ω-categorical theory T has the finite model property. The characterization makes it possible to transfer stability theoretic results in [29] to certain classes of finite structures. This approach also gives information concerning properties that a sequence of finite ``base structures'' of ever larger size must have in order for its random expansions to a larger vocabulary to have a chance to satisfy a convergence law for first-order logic.
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BibTeX
@misc{koponen2026characterization,
title = {{A characterization of the finite model property for $ω$-categorical theories}},
author = {Vera Koponen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16163},
eprint = {2610.16163},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16163},
}
RIS
TY - UNPB
TI - A characterization of the finite model property for ω-categorical theories
AU - Vera Koponen
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16163
UR - https://arxiv.org/abs/2610.16163
AB - A first-order theory T has the {\em finite model property} if every first-order sentence that is implied by T has a finite model. We give a characterization of when a complete ω-categorical theory T has the finite model property. The characterization makes it possible to transfer stability theoretic results in [29] to certain classes of finite structures. This approach also gives information concerning properties that a sequence of finite ``base structures'' of ever larger size must have in order for its random expansions to a larger vocabulary to have a chance to satisfy a convergence law for first-order logic.
ER -