Abstract
We prove a preservation theorem for NTP\(_1\) in the context of the generic variations construction. We also prove that NTP\(_1\) is preserved under adding to a geometric theory a generic predicate.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Baudisch, A.: Generic variations of models of T. J. Symb. Log. 67, 1025–1038 (2002)
Chatzidakis, Z., Pillay, A.: Generic structures and simple theories. Ann. Pure Appl. Log. 95, 71–92 (1998)
Chernikov, A.: Theories without the tree property of the second kind. Ann. Pure Appl. Log. 165, 695–723 (2014)
Chernikov, A., Ramsey, N.: On model-theoretic tree properties. J. Math. Log. https://doi.org/10.1142/S0219061316500094
Dobrowolski, J., Kim, H.: A preservation theorem for theories without the tree property of the first kind. Math. Log. Q 63(6), 536–543
Dzamonja, M., Shelah, S.: On \(\triangleleft ^*\)-maximality. Ann. Pure Appl. Log. 125, 119–158 (2004)
Granger, N.: Stability, simplicity, and the model theory of bilinear forms. PhD thesis, University of Manchester (1999)
Hodges, W.: Model Theory, vol. 42. Cambridge Univerity Press, Cambridge (1993)
Winkler, P.: Model-completeness and Skolem expansions. In: Model Theory and Algebra, A Memorial Tribute to Abraham Robinson, LNM, vol. 498, Springer, Berlin, pp. 408–463 (1975)
Takeuchi, K., Tsuboi, A.: On the existence of indiscernible trees. Ann. Pure Appl. Log. 163, 1891–1902 (2012)
Author information
Authors and Affiliations
Corresponding author
Additional information
The author was supported by NCN Grant No. 2015/19/D/ST1/01174 and by Samsung Science Technology Foundation under Project Number SSTF-BA1301-03.
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Dobrowolski, J. Generic variations and NTP\(_1\). Arch. Math. Logic 57, 861–871 (2018). https://doi.org/10.1007/s00153-018-0609-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00153-018-0609-4