Zobrazeno 1 - 10
of 14
pro vyhledávání: '"Nicholas Ramsey"'
Publikováno v:
Forum of Mathematics, Sigma, Vol 12 (2024)
We initiate a systematic study of generic stability independence and introduce the class of treeless theories in which this notion of independence is particularly well behaved. We show that the class of treeless theories contains both binary theories
Externí odkaz:
https://doaj.org/article/be195298dab149598b12fe77ce03a071
Autor:
Nicholas Ramsey, Itay Kaplan
Publikováno v:
Journal of the European Mathematical Society. 22:1423-1474
We study NSOP$_{1}$ theories. We define Kim-independence, which generalizes non-forking independence in simple theories and corresponds to non-forking at a generic scale. We show that Kim-independence satisfies a version of Kim's lemma, local charact
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::d8ead3ceddd2b817c9f14b01d57f91f2
https://doi.org/10.4171/jems/948
https://doi.org/10.4171/jems/948
We use exact saturation to study the complexity of unstable theories, showing that a variant of this notion called pseudo-elementary class (PC)-exact saturation meaningfully reflects combinatorial dividing lines. We study PC-exact saturation for stab
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2b6e289a653688cbc1a3ef534dc6b2b9
http://arxiv.org/abs/2009.08365
http://arxiv.org/abs/2009.08365
Publikováno v:
Proceedings of the American Mathematical Society. 147:1719-1732
We show that NSOP$_{1}$ theories are exactly the theories in which Kim-independence satisfies a form of local character. In particular, we show that if $T$ is NSOP$_{1}$, $M\models T$, and $p$ is a type over $M$, then the collection of elementary sub
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::297d3d3535ca0718757c14ef060b3576
https://doi.org/10.1090/proc/14305
https://doi.org/10.1090/proc/14305
Publikováno v:
Annals of Pure and Applied Logic. 173:103058
We study Kim-independence over arbitrary sets. Assuming that forking satisfies existence, we establish Kim's lemma for Kim-dividing over arbitrary sets in an NSOP1 theory. We deduce symmetry of Kim-independence and the independence theorem for Lascar
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::99083456e9a6750b4c6c58925f1cae26
https://doi.org/10.1016/j.apal.2021.103058
https://doi.org/10.1016/j.apal.2021.103058
Publikováno v:
Annals of Pure and Applied Logic. 172:102992
We introduce the class of unshreddable theories, which contains the simple and NIP theories, and prove that such theories have exactly saturated models in singular cardinals, satisfying certain set-theoretic hypotheses. We also give criteria for a th
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::32cccb6abf208196527985895a09c2a0
https://doi.org/10.1016/j.apal.2021.102992
https://doi.org/10.1016/j.apal.2021.102992
Autor:
Nicholas Ramsey, Itay Kaplan
We prove several results on the behavior of Kim-independence upon changing the base in NSOP$_{1}$ theories. As a consequence, we prove that Kim-independence satisfies transitivity and that this characterizes NSOP$_{1}$. Moreover, we characterize witn
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a9128c33f8d22b80c2248c07a0f8c2d7
http://arxiv.org/abs/1901.07026
http://arxiv.org/abs/1901.07026
Autor:
Nicholas Ramsey
We prove that, in order to establish that a theory is NSOP1, it suffices to show that no formula in a single free variable has SOP1.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e6997f21b9f7533b656fba7dd4323e75
Autor:
Nicholas Ramsey, Alex Kruckman
We study expansions of NSOP 1 theories that preserve NSOP 1 . We prove that if T is a model complete NSOP 1 theory eliminating the quantifier ∃ ∞ , then the generic expansion of T by arbitrary constant, function, and relation symbols is still NSO
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0336f648a42cae316caa9ecd7148ef24
Autor:
Nicholas Ramsey
We consider global analogues of model-theoretic tree properties. The main objects of study are the invariants related to Shelah's tree property $\kappa_{\text{cdt}}(T)$, $\kappa_{\text{sct}}(T)$, and $\kappa_{\text{inp}}(T)$ and the relations that ob
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::cfc551a08740d6abb04d748ed141e593