اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدOn perturbations of Hilbert spaces and probability algebras with a generic automorphism
120
0
0.0
(
0
)
تأليف
Itai Ben Yaacov
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We prove that $IHS_A$, the theory of infinite dimensional Hilbert spaces equipped with a generic automorphism, is $aleph_0$-stable up to perturbation of the automorphism, and admits prime models up to perturbation over any set. Similarly, $APr_A$, the theory of atomless probability algebras equipped with a generic automorphism is $aleph_0$-stable up to perturbation. However, not allowing perturbation it is not even superstable.
قيم البحث
اقرأ أيضاً
We study the model theory of expansions of Hilbert spaces by generic predicates. We first prove the existence of model companions for generic expansions of Hilbert spaces in the form first of a distance function to a random substructure, then a dista
nce to a random subset. The theory obtained with the random substructure is {omega}-stable, while the one obtained with the distance to a random subset is $TP_2$ and $NSOP_1$. That example is the first continuous structure in that class.
We introduce the notion of $Delta$ and $sigma,Delta-$ pairs for operator algebras and characterise $Delta-$ pairs through their categories of left operator modules over these algebras. Furthermore, we introduce the notion of $Delta$-Morita equivalent
operator spaces and prove a similar theorem about their algebraic extensions. We prove that $sigmaDelta$-Morita equivalent operator spaces are stably isomorphic and vice versa. Finally, we study unital operator spaces, emphasising their left (resp. right) multiplier algebras, and prove theorems that refer to $Delta$-Morita equivalence of their algebraic extensions.
Probability logic has contributed to significant developments in belief types for game-theoretical economics. We present a new probability logic for Harsanyi Type spaces, show its completeness, and prove both a de-nesting property and a unique extens
ion theorem. We then prove that multi-agent interactive epistemology has greater complexity than its single-agent counterpart by showing that if the probability indices of the belief language are restricted to a finite set of rationals and there are finitely many propositional letters, then the canonical space for probabilistic beliefs with one agent is finite while the canonical one with at least two agents has the cardinality of the continuum. Finally, we generalize the three notions of definability in multimodal logics to logics of probabilistic belief and knowledge, namely implicit definability, reducibility, and explicit definability. We find that S5-knowledge can be implicitly defined by probabilistic belief but not reduced to it and hence is not explicitly definable by probabilistic belief.
We give a model-theoretic treatment of the fundamental results of Kechris-Pestov-Todorv{c}evi{c} theory in the more general context of automorphism groups of not necessarily countable structures. One of the main points is a description of the univers
al ambit as a certain space of types in an expanded language. Using this, we recover various results of Kechris-Pestov-Todorv{c}evi{c}, Moore, Ngyuen Van Th{e}, in the context of automorphism groups of not necessarily countable structures, as well as Zucker.
We will review the main results concerning the automorphism groups of saturated structures which were obtained during the two last decades. The main themes are: the small index property in the countable and uncountable cases; the possibility of recov
ering a structure or a significant part of it from its automorphism group; the subgroup of strong automorphisms.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
