Cohen-like first order structures

0560281 - MÚ 2024 RIV NL eng J - Článek v odborném periodiku
Kostana, Ziemowit
Cohen-like first order structures.
Annals of Pure and Applied Logic. Roč. 174, č. 1 (2023), č. článku 103172. ISSN 0168-0072. E-ISSN 1873-2461
Grant CEP: GA ČR(CZ) GX20-31529X
Institucionální podpora: RVO:67985840
Klíčová slova: Cohen forcing * Fraisse limit * generic structure * homogeneous structure
Obor OECD: Pure mathematics
Impakt faktor: 0.8, rok: 2022
Způsob publikování: Omezený přístup
https://doi.org/10.1016/j.apal.2022.103172

We study uncountable structures similar to the Fraïssé limits. The standard inductive arguments from the Fraïssé theory are replaced by forcing, so the structures we obtain are highly sensitive to the universe of set theory. In particular, the generic structures we investigate exist only in generic extensions of the universe. We prove that in most of the interesting cases the uncountable generic structures are rigid. Moreover, we provide a (consistent) example of an uncountable, dense set of reals with the group of integers as its automorphism group.
Trvalý link: https://hdl.handle.net/11104/0333268