Results for 'AL*‐algebra'

1000+ found
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  1.  19
    Review: Arthur N. Prior, Edward C. Moore, Richard S. Robin, The Algebra of the Copula. [REVIEW]Alan Ross Anderson - 1974 - Journal of Symbolic Logic 39 (2):354-354.
  2.  54
    Free set algebras satisfying systems of equations.G. Aldo Antonelli - 1999 - Journal of Symbolic Logic 64 (4):1656-1674.
    In this paper we introduce the notion of a set algebra S satisfying a system E of equations. After defining a notion of freeness for such algebras, we show that, for any system E of equations, set algebras that are free in the class of structures satisfying E exist and are unique up to a bisimulation. Along the way, analogues of classical set-theoretic and algebraic properties are investigated.
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  3.  54
    A Generalization of the Łukasiewicz Algebras.Teresa Almada & JÚlia Vaz de Carvalho - 2001 - Studia Logica 69 (3):329 - 338.
    We introduce the variety $\scr{L}_{n}^{m}$ , m ≥ 1 and n ≥ 2, of m-generalized Łukasiewicz algebras of order n and characterize its subdirectly irreducible algebras. The variety $\scr{L}_{n}^{m}$ is semisimple, locally finite and has equationally definable principal congruences. Furthermore, the variety $\scr{L}_{n}^{m}$ contains the variety of Łukasiewicz algebras of order n.
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  4.  23
    Kiyoshi Iséki. An algebra related with a propositional calculus. Proceedings of the Japan Academy, vol. 42 , pp. 26–29. - Yoshinari Arai, Kiyoshi Iséki, and Shôtarô Tanaka. Characterizations of BCI, BCK-algebras. Proceedings of the Japan Academy, vol. 42 , pp. 105–107. - Kiyoshi Iséki. Algebraic formulation of propositional calculi with general detachment rule. Proceedings of the Japan Academy, vol. 43 , pp. 31–34. [REVIEW]R. B. Angell - 1970 - Journal of Symbolic Logic 35 (3):465-466.
  5.  63
    Algebraic Logic, Where Does It Stand Today?Tarek Sayed Ahmed - 2005 - Bulletin of Symbolic Logic 11 (3):465-516.
    This is a survey article on algebraic logic. It gives a historical background leading up to a modern perspective. Central problems in algebraic logic (like the representation problem) are discussed in connection to other branches of logic, like modal logic, proof theory, model-theoretic forcing, finite combinatorics, and Gödel’s incompleteness results. We focus on cylindric algebras. Relation algebras and polyadic algebras are mostly covered only insofar as they relate to cylindric algebras, and even there we have not told the whole story. (...)
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  6.  27
    Günther Patzig. Einleitung. Logische Untersuchungen, by Gottlob Frege, edited by Günther Patzig, Vandenhoeck & Ruprecht, Göttingen1966, pp. 5–29. - Gottlob Frege. Der Gedanke. Eine logische Untersuchung. A reprint of XVIII 93. Logische Untersuchungen, by Gottlob Frege, edited by Günther Patzig, Vandenhoeck & Ruprecht, Göttingen1966, pp. 30–53. - Gottlob Frege. Die Verneinung. Eine logische Untersuchung. A reprint of XVIII 93. Logische Untersuchungen, by Gottlob Frege, edited by Günther Patzig, Vandenhoeck & Ruprecht, Göttingen1966, pp. 54–71. - Gottlob Frege. Logische Untersuchungen. Dritter Teil: Gedankengefüge.Logische Untersuchungen, by Gottlob Frege, edited by Günther Patzig, Vandenhoeck & Ruprecht, Göttingen1966, pp. 72–91. , pp. 36–51.) - Gottlob Frege. Kritische Beleuchtung einiger Punkte in E. Schröders Vorlesungen über die Algebra der Logik. A reprint of 4972. Ibid., pp. 92–112. - Gottlob Frege. Über die Zahlen des Herrn H. Schubert. A reprint of 4915. Logische Untersuchungen,. [REVIEW]I. Angelelli - 1968 - Journal of Symbolic Logic 33 (2):282-284.
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  7.  35
    Algebra and Theory of Order-Deterministic Pomsets.Arend Rensink - 1996 - Notre Dame Journal of Formal Logic 37 (2):283-320.
    This paper is about partially ordered multisets (pomsets for short). We investigate a particular class of pomsets that we call order-deterministic, properly including all partially ordered sets, which satisfies a number of interesting properties: among other things, it forms a distributive lattice under pomset prefix (hence prefix closed sets of order-deterministic pomsets are prime algebraic), and it constitutes a reflective subcategory of the category of all pomsets. For the order-deterministic pomsets we develop an algebra with a sound and (-) complete (...)
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  8.  9
    Σ‐algebraically compact modules and ‐compact cardinals.Jan Šaroch - 2015 - Mathematical Logic Quarterly 61 (3):196-201.
    We prove that the property characterizes Σ‐algebraically compact modules if is not ω‐measurable. Moreover, under a large cardinal assumption, we show that over any ring R where is not ω‐measurable, any free module M of ω‐measurable rank satisfies, hence the assumption on cannot be dropped in general (e.g., over small non‐right perfect rings). In this way, we extend results from a recent paper by Simion Breaz.
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  9.  24
    Some Boolean Algebras with Finitely Many Distinguished Ideals I.Regina Aragón - 1995 - Mathematical Logic Quarterly 41 (4):485-504.
    We consider the theory Thprin of Boolean algebras with a principal ideal, the theory Thmax of Boolean algebras with a maximal ideal, the theory Thac of atomic Boolean algebras with an ideal where the supremum of the ideal exists, and the theory Thsa of atomless Boolean algebras with an ideal where the supremum of the ideal exists. First, we find elementary invariants for Thprin and Thsa. If T is a theory in a first order language and α is a linear (...)
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  10.  20
    Some Boolean algebras with finitely many distinguished ideals II.Regina Aragón - 2003 - Mathematical Logic Quarterly 49 (3):260.
    We describe the countably saturated models and prime models of the theory Thprin of Boolean algebras with a principal ideal, the theory Thmax of Boolean algebras with a maximal ideal, the theory Thac of atomic Boolean algebras with an ideal such that the supremum of the ideal exists, and the theory Thsa of atomless Boolean algebras with an ideal such that the supremum of the ideal exists. We prove that there are infinitely many completions of the theory of Boolean algebras (...)
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  11.  34
    SICs and Algebraic Number Theory.Marcus Appleby, Steven Flammia, Gary McConnell & Jon Yard - 2017 - Foundations of Physics 47 (8):1042-1059.
    We give an overview of some remarkable connections between symmetric informationally complete measurements and algebraic number theory, in particular, a connection with Hilbert’s 12th problem. The paper is meant to be intelligible to a physicist who has no prior knowledge of either Galois theory or algebraic number theory.
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  12.  13
    A solution to identities problem in 2-element HSI-algebras.Gurgen R. Asatryan - 2004 - Mathematical Logic Quarterly 50 (2):175.
    All arithmetical identities involving 1, addition, multiplication and exponentiation are valid in every 2-element HSI-algebra.
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  13.  11
    On models of exponentiation. Identities in the HSI-algebra of posets.Gurgen Asatryan - 2008 - Mathematical Logic Quarterly 54 (3):280-287.
    We prove that Wilkie's identity holds in those natural HSI-algebras where each element has finite decomposition into components.Further, we construct a bunch of HSI-algebras that satisfy all the identities of the set of positive integers ℕ. Then, based on the constructed algebras, we prove that the identities of ℕ hold in the HSI-algebra of finite posets when the value of each variable is a poset having an isolated point.
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  14.  80
    The model theory of modules of a C*-algebra.Camilo Argoty - 2013 - Archive for Mathematical Logic 52 (5-6):525-541.
    We study the theory of a Hilbert space H as a module for a unital C*-algebra ${\mathcal{A}}$ from the point of view of continuous logic. We give an explicit axiomatization for this theory and describe the structure of all the representations which are elementary equivalent to it. Also, we show that this theory has quantifier elimination and we characterize the model companion of the incomplete theory of all non-degenerate representations of ${\mathcal{A}}$ . Finally, we show that there is an homeomorphism (...)
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  15.  25
    Frames and MV-Algebras.Lawrence P. Belluce & Antonio Di Nola - 2005 - Studia Logica 81 (3):357 - 385.
    We describe a class of MV-algebras which is a natural generalization of the class of "algebras of continuous functions". More specifically, we're interested in the algebra of frame maps $Hom_{\scr{F}}(\Omega (A),\text{K})$ in the category $\scr{F}$ of frames, where A is a topological MV-algebra, Ω(A) the lattice of open sets of A, and K an arbitrary frame. Given a topological space X and a topological MV-algebra A, we have the algebra C(X, A) of continuous functions from X to A. We can (...)
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  16.  17
    Intersections of algebraically closed fields.C. J. Ash & John W. Rosenthal - 1986 - Annals of Pure and Applied Logic 30 (2):103-119.
  17.  14
    Language as a complex algebra: Post-structuralism and inflectional morphology in Saussure’s Cours.Raúl Aranovich - 2016 - Semiotica 2016 (208).
    Name der Zeitschrift: Semiotica Jahrgang: 2016 Heft: 208 Seiten: 133-154.
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  18. Some Boolean Algebras with Finitely Many Distinguished Ideals I.Regina Arag N. - 1995 - Mathematical Logic Quarterly 41 (4):485-504.
     
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  19.  4
    Logic and Boolean Algebra.Theodore Hailperin - 1964 - Journal of Symbolic Logic 29 (2):95-96.
  20.  27
    Double Negation Semantics for Generalisations of Heyting Algebras.Rob Arthan & Paulo Oliva - 2020 - Studia Logica 109 (2):341-365.
    This paper presents an algebraic framework for investigating proposed translations of classical logic into intuitionistic logic, such as the four negative translations introduced by Kolmogorov, Gödel, Gentzen and Glivenko. We view these asvariant semanticsand present a semantic formulation of Troelstra’s syntactic criteria for a satisfactory negative translation. We consider how each of the above-mentioned translation schemes behaves on two generalisations of Heyting algebras: bounded pocrims and bounded hoops. When a translation fails for a particular class of algebras, we demonstrate that (...)
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  21.  17
    Some theories associated with algebraically closed fields.Chris Ash & John Rosenthal - 1980 - Journal of Symbolic Logic 45 (2):359-362.
  22.  37
    A sufficient condition for completability of partial combinatory algebras.Andrea Asperti & Agata Ciabattoni - 1997 - Journal of Symbolic Logic 62 (4):1209-1214.
    A Partial Combinatory Algebra is completable if it can be extended to a total one. In [1] it is asked (question 11, posed by D. Scott, H. Barendregt, and G. Mitschke) if every PCA can be completed. A negative answer to this question was given by Klop in [12, 11]; moreover he provided a sufficient condition for completability of a PCA (M, ·, K, S) in the form of ten axioms (inequalities) on terms of M. We prove that just one (...)
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  23.  2
    Logic in Algebraic Form. Three Languages and Theories.Stephen D. Comer - 1977 - Journal of Symbolic Logic 42 (1):108-109.
  24. Free Set Algebras Satisfying Systems of Equations.G. Antonelli - 1999 - Journal of Symbolic Logic 64 (4):1656-1674.
    In this paper we introduce the notion of a set algebra $\mathscr{S}$ satisfying a system $\mathscr{E}$ equations. After defining a notion of freeness for such algebras, we show that, for any system $\mathscr{E}$ of equations, set algebras that are free in the class of structures satisfying $\mathscr{E}$ exist and are unique up to a bisimulation. Along the way, analogues of classical set-theoretic and algebraic properties are investigated.
     
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  25. [Inverted form of Greek symbol Delta]-Structures, abstract algebras and structural analysis.K. Ashton - 1972 - Auckland, N.Z.,: University of Auckland, Dept. of Mathematics.
     
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  26.  21
    Properties of forking in {$ømega$}-free pseudo-algebraically closed fields.Zoé Chatzidakis - 2002 - Journal of Symbolic Logic 67 (3):957-996.
  27. AA. W., The Logico Algebraic Approach to Quantum Mechanics, voL II: Con-temporary Consolidation, ed. by CA. Hooker, D. Reidel Publ. Camp., Dor-drecht-Boston-London, 1979. AA. W., Theoretical Approaches to Complex Systems, Proceedings, Tubingen 1977, Lecture Notes in Biomathematics, 21, Springer-Veriag, Berlin 1978. [REVIEW]K. O. Apel - 1979 - International Logic Review 12 (19-24):156.
  28.  12
    Geometric reasoning with logic and algebra.Dennis S. Arnon - 1988 - Artificial Intelligence 37 (1-3):37-60.
  29.  29
    Forking and stability in the representations of a c*-algebra.Camilo Argoty - 2015 - Journal of Symbolic Logic 80 (3):785-796.
  30. The Development of Arabic Mathematics: Between Arithmetic and Algebra.A. F. W. Armstrong - 1994 - Boston Studies in the Philosophy of Science 156.
     
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  31.  19
    Decidable Regularly Closed Fields of Algebraic Numbers.Lou van den Dries & Rick L. Smith - 1985 - Journal of Symbolic Logic 50 (2):468 - 475.
  32.  12
    Independent Families in Complete Boolean Algebras.B. Balcar, F. Franek, Bohuslav Balcar, Jan Pelant, Petr Simon & Boban Velickovic - 2002 - Bulletin of Symbolic Logic 8 (4):554-554.
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  33.  10
    Square compactness and Lindelöf trees.Pedro E. Marun - forthcoming - Archive for Mathematical Logic:1-17.
    We prove that every weakly square compact cardinal is a strong limit cardinal, and therefore weakly compact. We also study Aronszajn trees with no uncountable finitely splitting subtrees, characterizing them in terms of being Lindelöf with respect to a particular topology. We prove that the class of such trees is consistently non-empty and lies between the classes of Suslin and Aronszajn trees.
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  34.  3
    Biogram.Janusz Czelakowski - 2024 - In Jacek Malinowski & Rafał Palczewski (eds.), Janusz Czelakowski on Logical Consequence. Springer Verlag. pp. 9-47.
    algebraic logic, universal algebra, action theory, infinitistic methods in the theory of definitions, algebraic methods in set theory, methods of mathematical logic in number theory.
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  35.  4
    Herbrandized modified realizability.Gilda Ferreira & Paulo Firmino - forthcoming - Archive for Mathematical Logic:1-19.
    Realizability notions in mathematical logic have a long history, which can be traced back to the work of Stephen Kleene in the 1940s, aimed at exploring the foundations of intuitionistic logic. Kleene’s initial realizability laid the ground for more sophisticated notions such as Kreisel’s modified realizability and various modern approaches. In this context, our work aligns with the lineage of realizability strategies that emphasize the accumulation, rather than the propagation of precise witnesses. In this paper, we introduce a new notion (...)
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  36.  10
    Review: J. Santos, H. Arango, La Operacion Puente en las Algebras de Boole. [REVIEW]Florencio G. Asenjo - 1969 - Journal of Symbolic Logic 34 (3):512-512.
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  37.  19
    Santos J. and Arango H.. La operación puente en las álgebras de Boole. Actas de las X jornadas, Unión Matemática Argentina, Instituto de Matemáticas, Universidad Nacional del Sur, Bahía Blanca 1957, pp. 25–28. [REVIEW]Florencio G. Asenjo - 1969 - Journal of Symbolic Logic 34 (3):512-512.
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  38.  13
    Cohesive powers of structures.Valentina Harizanov & Keshav Srinivasan - forthcoming - Archive for Mathematical Logic:1-24.
    A cohesive power of a structure is an effective analog of the classical ultrapower of a structure. We start with a computable structure, and consider its effective power over a cohesive set of natural numbers. A cohesive set is an infinite set of natural numbers that is indecomposable with respect to computably enumerable sets. It plays the role of an ultrafilter, and the elements of a cohesive power are the equivalence classes of certain partial computable functions determined by the cohesive (...)
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  39.  3
    Glivenko–Cantelli classes and NIP formulas.Karim Khanaki - forthcoming - Archive for Mathematical Logic:1-27.
    We give several new equivalences of NIP for formulas and new proofs of known results using Talagrand (Ann Probab 15:837–870, 1987) and Haydon et al. (in: Functional Analysis Proceedings, The University of Texas at Austin 1987–1989, Lecture Notes in Mathematics, Springer, New York, 1991). We emphasize that Keisler measures are more complicated than types (even in the NIP context), in an analytic sense. Among other things, we show that for a first order theory T and a formula $$\phi (x,y)$$, the (...)
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  40. The Fan Theorem, its strong negation, and the determinacy of games.Wim Veldman - forthcoming - Archive for Mathematical Logic:1-66.
    In the context of a weak formal theory called Basic Intuitionistic Mathematics $$\textsf{BIM}$$ BIM, we study Brouwer’s Fan Theorem and a strong negation of the Fan Theorem, Kleene’s Alternative (to the Fan Theorem). We prove that the Fan Theorem is equivalent to contrapositions of a number of intuitionistically accepted axioms of countable choice and that Kleene’s Alternative is equivalent to strong negations of these statements. We discuss finite and infinite games and introduce a constructively useful notion of determinacy. We prove (...)
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  41.  83
    On Particle Phenomenology Without Particle Ontology: How Much Local Is Almost Local?Aristidis Arageorgis & Chrysovalantis Stergiou - 2013 - Foundations of Physics 43 (8):969-977.
    Recently, Clifton and Halvorson have tried to salvage a particle phenomenology in the absence of particle ontology within algebraic relativistic quantum field theory. Their idea is that the detection of a particle is the measurement of a local observable which simulates the measurement of an almost local observable that annihilates the vacuum. In this note, we argue that the measurements local particle detections are supposed to simulate probe radically holistic aspects of relativistic quantum fields. We prove that in an axiomatic (...)
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  42.  1
    Álgebras de universales.José Tomás Alvarado Marambio - 2024 - Critica 56 (166):3-33.
    Varios filósofos han propuesto un enfoque “algebraico” de los universales de acuerdo con el cual hay operaciones de universales a universales. No es obvio, sin embargo, cómo estas operaciones deban ser interpretadas y qué impacto tengan para las condiciones de identidad de los universales. Hay dos interpretaciones principales del álgebra de universales. Por una parte, se ha interpretado como formas de “construir” universales complejos. Por otra, ha sido interpretada como “morfismos” o “mapeos” entre universales, pero no como algo que “construye” (...)
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  43.  20
    Nondefinability results with entire functions of finite order in polynomially bounded o-minimal structures.Hassan Sfouli - 2024 - Archive for Mathematical Logic 63 (3):491-498.
    Let \({\mathcal {R}}\) be a polynomially bounded o-minimal expansion of the real field. Let _f_(_z_) be a transcendental entire function of finite order \(\rho \) and type \(\sigma \in [0,\infty ]\). The main purpose of this paper is to show that if ( \(\rho ) or ( \(\rho =1\) and \(\sigma =0\) ), the restriction of _f_(_z_) to the real axis is not definable in \({\mathcal {R}}\). Furthermore, we give a generalization of this result for any \(\rho \in [0,\infty )\).
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  44.  7
    The extent of saturation of induced ideals.Kenta Tsukuura - forthcoming - Archive for Mathematical Logic:1-17.
    We construct a model with a saturated ideal _I_ over \({\mathcal {P}}_{\kappa }\lambda \) and study the extent of saturation of _I_.
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  45.  1
    Positive indiscernibles.Mark Kamsma - forthcoming - Archive for Mathematical Logic:1-20.
    We generalise various theorems for finding indiscernible trees and arrays to positive logic: based on an existing modelling theorem for s-trees, we prove modelling theorems for str-trees, str$$_0$$ 0 -trees (the reduct of str-trees that forgets the length comparison relation) and arrays. In doing so, we prove stronger versions for basing—rather than locally basing or EM-basing—str-trees on s-trees and str$$_0$$ 0 -trees on str-trees. As an application we show that a thick positive theory has k-$$\mathsf {TP_2}$$ TP 2 iff it (...)
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  46.  12
    On the extendability to $$\mathbf {\Pi }_3^0$$ ideals and Katětov order.Jialiang He, Jintao Luo & Shuguo Zhang - forthcoming - Archive for Mathematical Logic:1-6.
    We show that there is a $$ \varvec{\Sigma }_4^0$$ ideal such that it’s neither extendable to any $$ \varvec{\Pi }_3^0$$ ideal nor above the ideal $$ \textrm{Fin}\times \textrm{Fin} $$ in the sense of Katětov order, answering a question from M. Hrušák.
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  47.  6
    Around accumulation points and maximal sequences of indiscernibles.Moti Gitik - forthcoming - Archive for Mathematical Logic:1-18.
    Answering a question of Mitchell (Trans Am Math Soc 329(2):507–530, 1992) we show that a limit of accumulation points can be singular in $${\mathcal {K}}$$ K. Some additional constructions are presented.
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  48.  3
    On undecidability of the propositional logic of an associative binary modality.Michael Kaminski - forthcoming - Archive for Mathematical Logic:1-21.
    It is shown that both classical and intuitionistic propositional logics of an associative binary modality are undecidable. The proof is based on the deduction theorem for these logics.
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  49.  3
    Logica formale e logica trascendentale.Francesco Barone - 1957 - Torino,: Edizioni di "Filosofia".
    1. Da Leibniz a Kant.--2. L'algebra della logica.
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  50.  25
    Diagonal fixed points in algebraic recursion theory.Jordan Zashev - 2005 - Archive for Mathematical Logic 44 (8):973-994.
    The relation between least and diagonal fixed points is a well known and completely studied question for a large class of partially ordered models of the lambda calculus and combinatory logic. Here we consider this question in the context of algebraic recursion theory, whose close connection with combinatory logic recently become apparent. We find a comparatively simple and rather weak general condition which suffices to prove the equality of least fixed points with canonical (corresponding to those produced by the Curry (...)
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