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Model companion and model completion of theories of rings
Archive for Mathematical Logic, 2009The usual language for rings is augmented by, for each natural number \(k\), a \(k+1\)-ary relation symbol \(\text{rad}_k\), the intended interpretation of which is that \(\text{rad}_k(a, b_1, \dots, b_k)\) holds iff every maximal ideal which contains \(b_1,\dots, b_k\) also contains \(a\).
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Artificial Intelligence Model of an Smartphone-Based Virtual Companion
Lecture Notes in Computer Science, 2014 Part 3: Computational Methodologies for EntertainmentInternational audienceThis paper introduces an Artificial Intelligence (AI) model of a virtual companion system on smartphone.
Elham Saadatian +2 more
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The Model Companion of Stone Semilattices
Mathematical Logic Quarterly, 1991A pseudocomplemented semilattice is an algebra \((S;\land,^*,0)\) such that \((S;\land,0)\) is a meet semilattice with least element 0 and a unary operation \(^*\) satisfying \(z\land x=0\) iff \(z\leq x^*\) (with \(\leq\) denoting the canonical order in \(S\)).
Christoph Gerber, Jürg Schmid
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Model companions of theories of graphs
Mathematical Logic Quarterly, 2015We study model companions of theories extending the graph axioms. First we prove general results concerning the existence of the model companion. Then, by applying these results to the case of graphs, we give a series of companionable and non‐companionable examples.
Kota Takeuchi +2 more
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Personality model for a companion AIBO
Proceedings of the 2005 ACM SIGCHI International Conference on Advances in computer entertainment technology, 2005In this paper we describe the architecture that allows the modeling of an emotionally intelligent robot. We chose to implement these architectures on AIBO, which is a quadruped autonomous robot, developed by Sony. AIBO was developed as an entertainment robot with its "mind" resident on a memory stick.
Iulia Dobai +2 more
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The model-companion of a class of structures
Journal of Symbolic Logic, 1972If Σ is the class of all fields and Σ* is the class of all algebraically closed fields, then it is well known that Σ* is characterized by the following properties:(i) Σ* is the class of models of some first order theory K*.(ii) If m1m2 are in Σ* and m1 ⊆ m2 then m1 ≺ m2 (m1 is an elementary substructure of m2, i.e.
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Mathematical Logic Quarterly, 1989
Let \(K\) be a class of \({\mathcal L}\)-structures, and let \(H\) be a subclass of \(K\). Let \({\mathcal E}\) be the set of existential \({\mathcal L}\)-formulas. We define a positive integer \(\| \phi \|\) for each \(\phi\in {\mathcal E}\). For \(\eta,\eta'\in {\mathcal E}\) we say that \(\eta\) ' is an obstruction to \(\eta\) in \(H\) (modulo \(K\))
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Let \(K\) be a class of \({\mathcal L}\)-structures, and let \(H\) be a subclass of \(K\). Let \({\mathcal E}\) be the set of existential \({\mathcal L}\)-formulas. We define a positive integer \(\| \phi \|\) for each \(\phi\in {\mathcal E}\). For \(\eta,\eta'\in {\mathcal E}\) we say that \(\eta\) ' is an obstruction to \(\eta\) in \(H\) (modulo \(K\))
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Proceedings of the American Mathematical Society, 1975
We prove that the theory ZF has a model companion and we describe an axiom system for it. The notion of a model companion was introduced by E. Bers as a generalization of the notion of a model completion [3, ?5]. In this paper we prove that ZF has a model companion and describe a set of axioms for it.
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We prove that the theory ZF has a model companion and we describe an axiom system for it. The notion of a model companion was introduced by E. Bers as a generalization of the notion of a model completion [3, ?5]. In this paper we prove that ZF has a model companion and describe a set of axioms for it.
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On the model companion of partial differential fields with an automorphism [PDF]
Israel Journal of Mathematics, 2016 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 canonical base property, and ...
Omar Leon Sanchez +1 more
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