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Mathematical logic --- Frege, Gottlob --- Philosophy, German --- Logic, Modern --- Philosophie allemande --- Logique moderne --- Frege, Gottlob, --- Criticism and interpretation --- Critique et interprétation --- Frege, Gottlob (1848-1925) --- Philosophie --- --4434 --- Critique et interprétation --- Wijsgeren. (Reeks) --- Philosophie. (Collection) --- Philosophes. (Collection) --- Wijsbegeerte. (Reeks) --- --Philosophy, German --- --Wijsgeren. (Reeks) --- Frege, Gottlob, 1848-1925
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Henkin-Keisler models emanate from a modification of the Henkin construction introduced by Keisler to motivate the definition of ultraproducts. Keisler modified the Henkin construction at that point at which `new' individual constants are introduced and did so in a way that illuminates a connection between Henkin-Keisler models and ultraproducts. The resulting construction can be viewed both as a specialization of the Henkin construction and as an alternative to the ultraproduct construction. These aspects of the Henkin-Keisler construction are utilized here to present a perspective on ultraproducts and their applications accessible to the reader familiar with Henkin's proof of the completeness of first order logic and naive set theory. This approach culminates in proofs of various forms of the Keisler-Shelah characterizations of elementary equivalence and elementary classes via Henkin-Keisler models. The presentation is self-contained and proofs of more advanced results from set theory are introduced as needed. Audience: Logicians in philosophy, computer science, linguistics and mathematics.
Ultraproducts --- First-order logic --- Mathematics. --- Logic. --- Computer science. --- Mathematical logic. --- Mathematical Logic and Foundations. --- Computer Science, general. --- Logic, Symbolic and mathematical. --- Model theory --- Prime products --- Products, Prime --- Products, Ultra --- -Ultra-products --- Logic, Symbolic and mathematical --- Logic, Modern --- Informatics --- Science --- Argumentation --- Deduction (Logic) --- Deductive logic --- Dialectic (Logic) --- Logic, Deductive --- Intellect --- Philosophy --- Psychology --- Reasoning --- Thought and thinking --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Methodology --- Model theory. --- First-order logic.
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Logic, Modern --- Philosophy, Modern --- Logique moderne --- Philosophie moderne --- Kant, Immanuel, --- Hegel, Georg Wilhelm Friedrich, --- Deleuze, Gilles, --- Modern logic --- Deleuze, Gilles --- -Kant, Immanuel --- -Hegel, Georg Wilhelm Friedrich --- -Contributions in logic --- Contributions in logic --- Contributions in philosophy of history --- -Congresses --- Logic, Modern. --- -Hegel, Giorgio Guglielmo Frederico --- Kant, Emmanuel --- Kant, Emanuel --- Kant, Emanuele --- Hegel, Giorgio Guglielmo Frederico --- Hegel, Georg Wilhelm Friedrich --- Deleuze, G. --- Delëz, Zhilʹ, --- Dūlūz, Jīl, --- دولوز، جيل --- Hegel, Georg Wilhelm Friedrich. --- Kant, Immanuel --- Kant, I. --- Kānt, ʻAmmānūʼīl, --- Kant, Immanouel, --- Kant, Immanuil, --- Kʻantʻŭ, --- Kant, --- Kant, Emmanuel, --- Ḳanṭ, ʻImanuʼel, --- Kant, E., --- Kant, Emanuel, --- Cantơ, I., --- Kant, Emanuele, --- Kant, Im. --- קאנט --- קאנט, א. --- קאנט, עמנואל --- קאנט, עמנואל, --- קאנט, ע. --- קנט --- קנט, עמנואל --- קנט, עמנואל, --- كانت ، ايمانوئل --- كنت، إمانويل، --- カントイマニユエル, --- Kangde, --- 康德, --- Kanṭ, Īmānwīl, --- كانط، إيمانويل --- Kant, Manuel, --- Delezi, Jier, --- Hēgeru, --- Hei-ko-erh, --- Gegelʹ, Georg, --- Hījil, --- Khegel, --- Hegel, G. W. F. --- Hegel, --- Hei Ge Er, --- Chenkel, --- Hīghil, --- הגל, --- הגל, גאורג וילהלם פרידריך, --- הגל, גיאורג וילהלם פרידריך, --- הגל, ג.ו.פ, --- היגל, גורג ווילהלם פרדריך, --- היגל, גיורג וילהלם פרידריך, --- 黑格尔, --- Hegel, Guillermo Federico, --- Hegel, Jorge Guillermo Federico, --- Heyel, Georg Wilhelm Friedrich, --- Higil, Gʼūrg Vīlhim Frīdrīsh, --- هگل, --- هگل، گئورگ ويلهم فريدريش, --- Catégories (philosophie)
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