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  1. A. Lewin Renato, F. Mikenberg Irene & G. Schwarze Marı́a (2001). On Free Annotated Algebras. Annals of Pure and Applied Logic 108 (1):249-259.
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  2. A. R. A. (1956). Théorie Métamathématique des Idéaux. Review of Metaphysics 9 (4):709-709.
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  3. M. Abad, J. P. D.\'{\I.}az Varela & M. Zander (2003). Boolean Algebras With A Distinguished Automorphism. Reports on Mathematical Logic:101-112.
    In this paper we investigate a subvariety $\BA$ of tense algebras, which we call Boolean algebras with a distinguished automorphism. This variety provides a unifying framework for the algebras studied by Monteiro in [4] and by Moisil in [5,6]. Among others we prove that $\BA$ is generated by its finite members and we characterize the locally finite subvarieties of $\BA$.
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  4. Manuel Abad, Diego Castaño & José P. Díaz Varela (2010). Zariski‐Type Topology for Implication Algebras. Mathematical Logic Quarterly 56 (3):299-309.
    In this work we provide a new topological representation for implication algebras in such a way that its one-point compactification is the topological space given in [1]. Some applications are given thereof.
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  5. Manuel Abad, Alicia Fernandez & Nelli Meske (1996). Free Boolean Correlations Lattices. Reports on Mathematical Logic:2-11.
    In this paper we study some algebraic properties of the variety of Boolean correlation lattices. We give a characterization of congruences and simple algebras of the variety and we describe the algebra with a finite set of free generators.
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  6. Tarek Sayed Ahmed (2009). A Simple Construction of Representable Relation Algebras with Non‐Representable Completions. Mathematical Logic Quarterly 55 (3):237-244.
    We give a simple new construction of representable relation algebras with non-representable completions. Using variations on our construction, we show that the elementary closure of the class of completely representable relation algebras is not finitely axiomatizable.
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  7. Tarek Sayed Ahmed (2008). Amalgamation for Reducts of Polyadic Equality Algebras, a Negative Result. Bulletin of the Section of Logic 37 (1):37-50.
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  8. Tarek Sayed Ahmed (2008). Classes of Representable Algebras with the Amalgamation Property. Bulletin of the Section of Logic 37 (2):115-121.
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  9. John Allsup & Richard Kaye (2007). Normal Subgroups of Nonstandard Symmetric and Alternating Groups. Archive for Mathematical Logic 46 (2):107-121.
    Let ${\mathfrak{M}}$ be a nonstandard model of Peano Arithmetic with domain M and let ${n \in M}$ be nonstandard. We study the symmetric and alternating groups S n and A n of permutations of the set ${\{0,1,\ldots,n-1\}}$ internal to ${\mathfrak{M}}$ , and classify all their normal subgroups, identifying many externally defined such normal subgroups in the process. We provide evidence that A n and S n are not split extensions by these normal subgroups, by showing that any such complement if (...)
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  10. María E. Alonso, Henri Lombardi & Hervé Perdry (2008). Elementary Constructive Theory of Henselian Local Rings. Mathematical Logic Quarterly 54 (3):253-271.
    We give an elementary theory of Henselian local rings and construct the Henselisation of a local ring. All our theorems have an algorithmic content.
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  11. Donald A. Alton & E. W. Madison (1973). Computability of Boolean Algebras and Their Extensions. Annals of Mathematical Logic 6 (2):95-128.
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  12. Mohamed Amer & Tarek Sayed Ahmed (2006). Polyadic and Cylindric Algebras of Sentences. Mathematical Logic Quarterly 52 (5):444-449.
    In this note we give an interpretation of cylindric algebras as algebras of sentences of first order logic. We show that the isomorphism types of such algebras of sentences coincide with the class of neat reducts of cylindric algebras. Also we show how this interpretation sheds light on some recent results. This is done by likening Henkin's Neat Embedding Theorem to his celebrated completeness proof.
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  13. Beatrice Amrhein (1995). Aspects of Universal Algebra in Combinatory Logic. In Erwin Engeler (ed.), The Combinatory Programme. Birkhäuser 31--45.
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  14. Hajnal Andreka, Peter Burmeister & Istvan Nemeti (1980). Quasi Equational Logic Of Partial Algebras. Bulletin of the Section of Logic 9 (4):193-197.
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  15. Andrew Arana (2016). Imagination in Mathematics. In Amy Kind (ed.), The Routledge Handbook of Philosophy of Imagination. Routledge 463-477.
  16. Jeremy Avigad, Notes on a Formalization of the Prime Number Theorem.
    On September 6, 2004, using the Isabelle proof assistant, I verified the following statement: (%x. pi x * ln (real x) / (real x)) ----> 1 The system thereby confirmed that the prime number theorem is a consequence of the axioms of higher-order logic together with an axiom asserting the existence of an infinite set. All told, our number theory session, including the proof of the prime number theorem and supporting libraries, constitutes 673 pages of proof scripts, or roughly 30,000 (...)
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  17. Jeremy Avigad (2006). Methodology and Metaphysics in the Development of Dedekind's Theory of Ideals. In Jose Ferreiros Jeremy Gray (ed.), The architecture of modern mathematics.
    Philosophical concerns rarely force their way into the average mathematician’s workday. But, in extreme circumstances, fundamental questions can arise as to the legitimacy of a certain manner of proceeding, say, as to whether a particular object should be granted ontological status, or whether a certain conclusion is epistemologically warranted. There are then two distinct views as to the role that philosophy should play in such a situation. On the first view, the mathematician is called upon to turn to the counsel (...)
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  18. Michael Beeson (1976). The Unprovability in Intuitionistic Formal Systems of the Continuity of Effective Operations on the Reals. Journal of Symbolic Logic 41 (1):18-24.
  19. Alexander Berenstein (2004). Dividing in the Algebra of Compact Operators. Journal of Symbolic Logic 69 (3):817-829.
    We interpret the algebra of finite rank operators as imaginaries inside a Hilbert space. We prove that the Hilbert space enlarged with these imaginaries has built-in canonical bases.
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  20. Xavier Caicedo & Roberto Cignoli (2001). An Algebraic Approach to Intuitionistic Connectives. Journal of Symbolic Logic 66 (4):1620-1636.
    It is shown that axiomatic extensions of intuitionistic propositional calculus defining univocally new connectives, including those proposed by Gabbay, are strongly complete with respect to valuations in Heyting algebras with additional operations. In all cases, the double negation of such a connective is equivalent to a formula of intuitionistic calculus. Thus, under the excluded third law it collapses to a classical formula, showing that this condition in Gabbay's definition is redundant. Moreover, such connectives can not be interpreted in all Heyting (...)
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  21. Sergio A. Celani & Hernán J. San Martín (2012). Frontal Operators in Weak Heyting Algebras. Studia Logica 100 (1-2):91-114.
    In this paper we shall introduce the variety FWHA of frontal weak Heyting algebras as a generalization of the frontal Heyting algebras introduced by Leo Esakia in [ 10 ]. A frontal operator in a weak Heyting algebra A is an expansive operator τ preserving finite meets which also satisfies the equation $${\tau(a) \leq b \vee (b \rightarrow a)}$$, for all $${a, b \in A}$$. These operators were studied from an algebraic, logical and topological point of view by Leo Esakia (...)
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  22. Roger M. Cooke & Michiel Lambalgen (1983). The Representation of Takeuti's *20c ||_ -Operator. Studia Logica 42 (4):407 - 415.
    Gaisi Takeuti has recently proposed a new operation on orthomodular lattices L, ⫫: $\scr{P}(L)\rightarrow L$ . The properties of ⫫ suggest that the value of ⫫ $(A)(A\subseteq L)$ corresponds to the degree in which the elements of A behave classically. To make this idea precise, we investigate the connection between structural properties of orthomodular lattices L and the existence of two-valued homomorphisms on L.
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  23. Steven H. Cullinane (2012). Notes on Groups and Geometry, 1978-1986. Internet Archive.
    Typewritten notes on groups and geometry.
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  24. Maarten de Rijke & Yde Venema (1995). Sahlqvist's Theorem for Boolean Algebras with Operators with an Application to Cylindric Algebras. Studia Logica 54 (1):61-78.
    For an arbitrary similarity type of Boolean Algebras with Operators we define a class ofSahlqvist identities. Sahlqvist identities have two important properties. First, a Sahlqvist identity is valid in a complex algebra if and only if the underlying relational atom structure satisfies a first-order condition which can be effectively read off from the syntactic form of the identity. Second, and as a consequence of the first property, Sahlqvist identities arecanonical, that is, their validity is preserved under taking canonical embedding algebras. (...)
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  25. Janet Folina (2012). Newton and Hamilton: In Defense of Truth in Algebra. Southern Journal of Philosophy 50 (3):504-527.
    Although it is clear that Sir William Rowan Hamilton supported a Kantian account of algebra, I argue that there is an important sense in which Hamilton's philosophy of mathematics can be situated in the Newtonian tradition. Drawing from both Niccolo Guicciardini's (2009) and Stephen Gaukroger's (2010) readings of the Newton–Leibniz controversy over the calculus, I aim to show that the very epistemic ideals that underpin Newton's argument for the superiority of geometry over algebra also motivate Hamilton's philosophy of algebra. Namely, (...)
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  26. Josep M. Font & Ventura Verdú (1993). The Lattice of Distributive Closure Operators Over an Algebra. Studia Logica 52 (1):1 - 13.
    In our previous paper Algebraic Logic for Classical Conjunction and Disjunction we studied some relations between the fragmentL of classical logic having just conjunction and disjunction and the varietyD of distributive lattices, within the context of Algebraic Logic. The central tool in that study was a class of closure operators which we calleddistributive, and one of its main results was that for any algebraA of type (2,2) there is an isomorphism between the lattices of allD-congruences ofA and of all distributive (...)
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  27. Han Geurdes, The Construction of Transfinite Equivalence Algorithms.
    Context: Consistency of mathematical constructions in numerical analysis and the application of computerized proofs in the light of the occurrence of numerical chaos in simple systems. Purpose: To show that a computer in general and a numerical analysis in particular can add its own peculiarities to the subject under study. Hence the need of thorough theoretical studies on chaos in numerical simulation. Hence, a questioning of what e.g. a numerical disproof of a theorem in physics or a prediction in numerical (...)
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  28. Burghard Herrmann (1997). Characterizing Equivalential and Algebraizable Logics by the Leibniz Operator. Studia Logica 58 (2):305-323.
    In [14] we used the term finitely algebraizable for algebraizable logics in the sense of Blok and Pigozzi [2] and we introduced possibly infinitely algebraizable, for short, p.i.-algebraizable logics. In the present paper, we characterize the hierarchy of protoalgebraic, equivalential, finitely equivalential, p.i.-algebraizable, and finitely algebraizable logics by properties of the Leibniz operator. A Beth-style definability result yields that finitely equivalential and finitely algebraizable as well as equivalential and p.i.-algebraizable logics can be distinguished by injectivity of the Leibniz operator. Thus, (...)
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  29. Jose Ferreiros Jeremy Gray (ed.) (2006). The Architecture of Modern Mathematics.
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  30. Ladislav Kvasz (2006). The History of Algebra and the Development of the Form of its Language. Philosophia Mathematica 14 (3):287-317.
    This paper offers an epistemological reconstruction of the historical development of algebra from al-Khwrizm, Cardano, and Descartes to Euler, Lagrange, and Galois. In the reconstruction it interprets the algebraic formulas as a symbolic language and analyzes the changes of this language in the course of history. It turns out that the most fundamental epistemological changes in the development of algebra can be interpreted as changes of the pictorial form of the symbolic language of algebra. Thus the paper develops further the (...)
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  31. Jean-Pierre Marquis (2013). Mathematical Forms and Forms of Mathematics: Leaving the Shores of Extensional Mathematics. Synthese 190 (12):2141-2164.
    In this paper, I introduce the idea that some important parts of contemporary pure mathematics are moving away from what I call the extensional point of view. More specifically, these fields are based on criteria of identity that are not extensional. After presenting a few cases, I concentrate on homotopy theory where the situation is particularly clear. Moreover, homotopy types are arguably fundamental entities of geometry, thus of a large portion of mathematics, and potentially to all mathematics, at least according (...)
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  32. Jean-pierre Marquis (1997). Abstract Mathematical Tools and Machines for Mathematics. Philosophia Mathematica 5 (3):250-272.
    In this paper, we try to establish that some mathematical theories, like K-theory, homology, cohomology, homotopy theories, spectral sequences, modern Galois theory (in its various applications), representation theory and character theory, etc., should be thought of as (abstract) machines in the same way that there are (concrete) machines in the natural sciences. If this is correct, then many epistemological and ontological issues in the philosophy of mathematics are seen in a different light. We concentrate on one problem which immediately follows (...)
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  33. Robert K. Meyer (2008). Ai, Me and Lewis (Abelian Implication, Material Equivalence and C I Lewis 1920). Journal of Philosophical Logic 37 (2):169 - 181.
    C I Lewis showed up Down Under in 2005, in e-mails initiated by Allen Hazen of Melbourne. Their topic was the system Hazen called FL (a Funny Logic), axiomatized in passing in Lewis 1921. I show that FL is the system MEN of material equivalence with negation. But negation plays no special role in MEN. Symbolizing equivalence with → and defining ∼A inferentially as A→f, the theorems of MEN are just those of the underlying theory ME of pure material equivalence. (...)
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  34. Alejandro Petrovich (1996). Distributive Lattices with an Operator. Studia Logica 56 (1-2):205 - 224.
    It was shown in [3] (see also [5]) that there is a duality between the category of bounded distributive lattices endowed with a join-homomorphism and the category of Priestley spaces endowed with a Priestley relation. In this paper, bounded distributive lattices endowed with a join-homomorphism, are considered as algebras and we characterize the congruences of these algebras in terms of the mentioned duality and certain closed subsets of Priestley spaces. This enable us to characterize the simple and subdirectly irreducible algebras. (...)
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  35. Charles C. Pinter (1975). Algebraic Logic with Generalized Quantifiers. Notre Dame Journal of Formal Logic 16 (4):511-516.
  36. Dhruv Raina (1996). Reconfiguring the Centre: The Structure of Scientific Exchanges Between Colonial India and Europe. Minerva 34 (2):161-176.
    The “centre-periphery” relationship historically structured scientific exchanges between metropolis and province, between the fount of empire and its outposts. But the exchange, if regarded merely as a one-way flow of scientific information, ignores both the politics of knowledge and the nature of its appropriation. Arguably, imperial structures do not entirely determine scientific practices and the exchange of knowledge. Several factors neutralise the over-determining influence of politics—and possibly also the normative values of science—on scientific practice.In examining these four examples of Indian (...)
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  37. Dhruv Raina (1992). Mathematical Foundations of a Cultural Project or Ramchandra's Treatise “Through the Unsentimentalised Light of Mathematics”. Historia Mathematica 19 (4).
    The nineteenth century witnessed a number of projects of cultural rapprochement between the knowledge traditions of the East and West. This paper discusses the attempt to render elementary calculus amenable to an Indian audience in the indigenous mathematical idiom, undertaken by an Indian polymath, Ramchandra. The exercise is specifically located in his book A Treatise on the Problems of Maxima and Minima. The paper goes on to discuss the “vocation of failure” of the book within the context of encounter and (...)
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  38. Dirk Schlimm (2008). On Abstraction and the Importance of Asking the Right Research Questions: Could Jordan Have Proved the Jordan-Hölder Theorem? [REVIEW] Erkenntnis 68 (3):409 - 420.
    In 1870 Jordan proved that the composition factors of two composition series of a group are the same. Almost 20 years later Hölder (1889) was able to extend this result by showing that the factor groups, which are quotient groups corresponding to the composition factors, are isomorphic. This result, nowadays called the Jordan-Hölder Theorem, is one of the fundamental theorems in the theory of groups. The fact that Jordan, who was working in the framework of substitution groups, was able to (...)
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  39. G. Spencer-Brown (1972). Laws of Form. New York,Julian Press.
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  40. Iulian D. Toader (2012). Fictionalism and Mathematical Objectivity. In Metaphysics and Science. Festschrift for Professor Ilie Pârvu. University of Bucharest Press 137-158.
  41. Alasdair Urquhart (1979). Distributive Lattices with a Dual Homomorphic Operation. Studia Logica 38 (2):201 - 209.
    The lattices of the title generalize the concept of a De Morgan lattice. A representation in terms of ordered topological spaces is described. This topological duality is applied to describe homomorphisms, congruences, and subdirectly irreducible and free lattices in the category. In addition, certain equational subclasses are described in detail.
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  42. Andrzej Wroński (2004). The Distance Function in Commutative ℓ-Semigroups and the Equivalence in Łukasiewicz Logic. Studia Logica 77 (2):241 - 253.
    The equivalence connective in ukasiewicz logic has its algebraic counterpart which is the distance function d(x,y) =|x–y| of a positive cone of a commutative -group. We make some observations on logically motivated algebraic structures involving the distance function.
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