Abstract
We present a relatively simple description of binary, definable subsets of models of weakly quasi-o-minimal theories. In particular, we closely describe definable linear orders and prove a weak version of the monotonicity theorem. We also prove that weak quasi-o-minimality of a theory with respect to one definable linear order implies weak quasi-o-minimality with respect to any other such order.
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Acknowledgements
The present paper is a considerably modified version of the preprint named Monotone theories [5]. It was written according to numerous comments and suggestions from the Referee, to whom we are greatly grateful as her/his help significantly improved the quality of the paper.
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The first author was supported by the Narodowe Centrum Nauki grant no. 2016/22/E/ST1/00450, and by the Ministry of Education, Science and Technological Development of Serbia through University of Belgrade, Faculty of Mathematics.
The second author was supported by the Ministry of Education, Science and Technological Development of Serbia through Mathematical Institute of the Serbian Academy of Sciences and Arts.
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Moconja, S., Tanović, P. Does weak quasi-o-minimality behave better than weak o-minimality?. Arch. Math. Logic 61, 81–103 (2022). https://doi.org/10.1007/s00153-021-00778-3
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DOI: https://doi.org/10.1007/s00153-021-00778-3