Hirotaka Kikyo
For a theory $T$ in $L, T_σ$ is the theory of the models of $T$ with an automorphism $σ$. If $T$ is an unstable model complete theory without the independence property, then $T_σ$ has no model companion. If $T$ is an unstable model complete theory and $T_σ$ has the amalgamation property, then $T_σ$ has no model companion. If $T$ is model complete and has the fcp, then $T_σ$ has no model completion.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
We prove that the class of partial differential fields of characteristic zero with an automorphism has a model companion. We then establish the basic model theoretic properties of this theory and prove that it satisfies the Zilber dichotomy for finite dimensional minimal types.
Kikyo and Shelah showed that if $T$ is a theory with the Strict Order Property in some first-order language $\mathcal{L}$, then in the expanded language $\mathcal{L}_σ:= \mathcal{L}\cup\{σ\}$ with a new unary function symbol $σ$, the bigger theory $T_σ:= T\cup\{``σ\mbox{is an} \mathcal{L}\mbox{-automorphism''}\}$ does not have a model companion. We show in this paper that if, however, we restrict the automorphism and consider the theory $T_σ$ as the base theory $T$ together with a ``restricted'' class of automorphisms, then $T_σ$ can have a model companion in $\mathcal{L}_σ$. We show this in t…
PAC fields and difference fields with generic automorphisms
本文研究域论添加自同构后模型伴生的存在性，证明两类情形（有界PAC域及ACFA的完备化）添加自同构后均无模型伴生，并给出显式障碍。
If T is an model complete theory with the strict order property, then the theory of the models of T with an automorphism has no model companion.
Abraham Robinson's method for finding model completions is refined and and generalized for model companions and is applied to the theory of fields equipped with both a valuation and an automorphism.
The theory of fields that are equipped with a countably infinite family of commuting derivations is not companionable; but if the axiom is added whereby the characteristic of the fields is zero, then the resulting theory is companionable. Each of these two theories is the union of a chain of companionable theories. In the case of characteristic zero, the model-companions of the theories in the chain form another chain, whose union is therefore the model-companion of the union of the original chain. However, in a signature with predicates, in all finite numbers of arguments, for linear dependen…
Testing definitional equivalence of theories via automorphism groups
本文提出一阶逻辑理论定义等价的充要条件为模型类间存在保同构和超积的双射，通过实例展示定义不等价但模型范畴具体同构的理论对，并解决了相关猜想。
Let G be a countable group. We proof that there is a model companion for the approximate theory of a Hilbert space with a group G of automorphisms. We show that G is amenable if and only if the structure induced by countable copies of the regular representation of G is existentially closed.
We study some dynamical aspects of the action of automorphisms in model theory in particular in the presence of invariant measures. We give some characterizations for NIP theories in terms of dynamics of automorphisms and invariant measures for example in terms of compact systems, entropy and measure algebras. Moreover, we study the concept of symbolic representation for models. Amongst the results, we give some characterizations for dividing lines and combinatorial configurations such as independence property, order property and strictly order property in terms of symbolic representations.
Simplicity of the automorphism group of fields with operators
本文改编 Lascar 的证明，证明了涵盖强极小理论和带算子域理论的一类不可数模型中，固定所有非泛型元素的自同构群具有单纯性。
We generalise the correspondence between $\aleph 0$-categorical theories and their automorphism groups to arbitrary complete theories in classical logic, and to some theories (including, in particular, all $\aleph 0$-categorical ones) in continuous logic.
E. Hrushovski proved tha the theory of difference-differential fields has a model companion. We prove this result and other maind properties of this theory that we call DCFA. We describe the SU rank a its relation with transcendence degree. We prove a version of Zilber's dichotomy and we give a description of Abelian definable groups.
We give an almost entirely model-theoretic account of both Ramsey classes of finite structures and of generalized indiscernibles as studied in special cases in (for example) [7], [9]. We understand "theories of indiscernibles" to be special kinds of companionable theories of finite structures, and much of the work in our arguments is carried in the context of the model-companion. Among other things, this approach allows us to prove that the companion of a theory of indiscernibles whose "base" consists of the quantifier-free formulas is necessarily the theory of the Fraisse limit of a Fraisse c…
We show that the generic automorphism is axiomatisable in the green field of Poizat (once Morleyised) as well as in the bad fields which are obtained by collapsing this green field to finite Morley rank. As a corollary, we obtain "bad pseudofinite fields" in characteristic 0. In both cases, we give geometric axioms. In fact, a general framework is presented allowing this kind of axiomatisation. We deduce from various constructibility results for algebraic varieties in characteristic 0 that the green and bad fields fall into this framework. Finally, we give similar results for other theories ob…
In this paper we continue the exploration of the classes of positively closed and h-maximal model of an h-inductive theory in the context of positive logic. In the section 2 we give a concrete description of the class of h-maximal models of an h-inductive theory and theirs companion theories. The section 3 is concerned to the study of the positive Robinson and locally positive Robinson theories and their connexion with the properties of the class of h-maximal models of the companion theories, and their connexion with the property of elimination of quantifiers. Before dealing with the topics me…
A structure ${\mathbb Y}$ of a relational language $L$ is called almost chainable iff there are a finite set $F \subset Y$ and a linear order $<$ on the set $Y\setminus F$ such that for each partial automorphism $φ$ (i.e., local automorphism, in Fra\"ıssé's terminology) of the linear order $\langle Y\setminus F, < \rangle$ the mapping ${\mathrm{id}} _F \cup φ$ is a partial automorphism of ${\mathbb Y}$. By a theorem of Fra\"ıssé, if $|L|<ω$, then ${\mathbb Y}$ is almost chainable iff the profile of ${\mathbb Y}$ is bounded; namely, iff there is a positive integer $m$ such that ${\mathbb Y}$ ha…
We study a class of first-order theories whose complete quantifier-free types with one free variable either have a trivial positive part or are isolated by a positive quantifier-free formula--plus a few other technical requirements. The theory of vector spaces and the theory fields are examples. We prove the amalgamation property and the existence of a model-companion. We show that the model-companion is strongly minimal. We also prove that the length of any increasing sequence of prime types is bounded, so every formula has finite Krull dimension.
Taking model-complete cores
本文研究了模型完全核心理论的性质，证明了稳定性、NIP等性质在核心伴生理论下的保持性，并探讨了不同结构理论类在核心伴生理论下的封闭性问题。
We prove that the theories of fields with Hasse-Schmidt derivations corresponding to actions of formal groups admit model companions. We also give geometric axiomatizations of these model companions.
Beth companions of finitary essentially algebraic theories
该研究针对局部有限呈现范畴构造Beth伴随，证明其唯一性，给出计算与句法表示方法，确立性质转移条件，为范畴论相关研究提供理论支撑。
Baumslag-Solitar Subgroups Obstruct Model Companions for Fields with Group Actions
该研究证明含Baumslag-Solitar子群BS(m,n)（mn≠0）的群，其带群作用的域无模型伴侣，解决了Beyarslan和Kowalski的猜想，还确定ℚ²等群的对应域无模型伴侣，改进了Hrushovski的相关方法。
Assume a complete superstable theory is superstable, and let P be a class of regular types, typically closed under automorphisms of the monster and non-orthogonality. We define the notion of P-NDOP and prove the existence of P-decompositions and derive an analog of Sh401 for superstable theories with P-NDOP. In this context, we also find a sufficient condition on P-decompositions that imply non-isomorphic models. For this, we investigate natural structures on the types in P\intersect S(M) modulo non-orthogonality.
Locally $\aleph_0$-categorical theories and locally Roelcke precompact groups
本文研究了局部 $\aleph_0$-范畴理论与局部罗尔克预紧群的对应关系，证明了它们的双可解释性及自同构群的同构性。
We present the notions of positively complete theory and general forms of amalgamation in the framework of positive logic. We explore the fundamental properties of positively complete theories and study the behaviour of companion theories by a change of constants in the language. Moreover, we present a general form of amalgamation and discuss some forms of strong amalgamation.
We define the interpolative fusion $T^*_\cup$ of a family $(T_i)_{i \in I}$ of first-order theories over a common reduct $T_\cap$, a notion that generalizes many examples of random or generic structures in the model-theoretic literature. When each $T_i$ is model-complete, $T^*_\cup$ coincides with the model companion of $T_\cup = \bigcup_{i \in I} T_i$. By obtaining sufficient conditions for the existence of $T^*_\cup$, we develop new tools to show that theories of interest have model companions.
In a previous paper we developed the notions of th-independence and þ-ranks which define a geometric independence relation in a class of theories which we called ``rosy''. We proved that rosy theories include simple and o-minimal theories and that for any theory for which the stable forking conjecture was true, þ-forking coincides with forking independence. In this article, we continue to study properties of th-forking and find more examples of rosy theories. Among the new properties we prove in this paper are some alternative characterizations of rosy theories and some tools to prove and anal…
Uniform terms and local elements
该研究从代数视角分析一致理论中项与谓词的一致性，关联域论与测度论，提出元素作为集合自同构的新解读及元素相对局部化方法，属于数理逻辑与代数交叉领域。
Existence of a Model Companion for Groups of Exponent 3
本文证明指数为3的群的理论具有模型伴生，验证了关于指数n的群理论模型伴生存在性猜想中n=3的情形，该猜想与Burnside问题的正解相关。
In a previous paper, the author and his collaborators studied the phenomenon of isotropy in the context of single-sorted equational theories, and showed that the isotropy group of the category of models of any such theory encodes a notion of inner automorphism for the theory. Using results from the treatment of combination problems in term rewriting theory, we show in this article that if $\mathbb{T}_1$ and $\mathbb{T}_2$ are (disjoint) equational theories satisfying minimal assumptions, then any free, finitely generated model of the disjoint union theory $\mathbb{T}_1 + \mathbb{T}_2$ has triv…
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 $\exists^{\infty}$, then the generic expansion of $T$ by arbitrary constant, function, and relation symbols is still NSOP$_1$. We give a detailed analysis of the special case of the theory of the generic $L$-structure, the model companion of the empty theory in an arbitrary language $L$. Under the same hypotheses, we show that $T$ may be generically expanded to an NSOP$_1$ theory with built-in Skolem functions. In order to obtain these results, we…
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。