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  1. Christian Wüthrich, Hajnal Andréka & István Németi, A Twist in the Geometry of Rotating Black Holes: Seeking the Cause of Acausality.
    We investigate Kerr–Newman black holes in which a rotating charged ring-shaped singularity induces a region which contains closed timelike curves (CTCs). Contrary to popular belief, it turns out that the time orientation of the CTC is oppo- site to the direction in which the singularity or the ergosphere rotates. In this sense, CTCs “counter-rotate” against the rotating black hole. We have similar results for all spacetimes sufficiently familiar to us in which rotation induces CTCs. This motivates our conjecture that perhaps (...)
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  2. Hajnal Andréka, Judit X. Madarász, István Németi & Gergely Székely (2012). A Logic Road From Special Relativity to General Relativity. Synthese 186 (3):633 - 649.
    We present a streamlined axiom system of special relativity in first-order logic. From this axiom system we "derive" an axiom system of general relativity in two natural steps. We will also see how the axioms of special relativity transform into those of general relativity. This way we hope to make general relativity more accessible for the non-specialist.
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  3. Hajnal Andréka, Judit X. Madarász, István Németi & Gergely Székely, A Logic Road From Special to General Relativity.
    We present a streamlined axiom system of special relativity in firs-order logic. From this axiom system we ``derive'' an axiom system of general relativity in two natural steps. We will also see how the axioms of special relativity transform into those of general relativity. This way we hope to make general relativity more accessible for the non-specialist.
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  4. Hajnal Andréka, Judit Madarász X., István Németi & Gergely Székely (2008). Axiomatizing Relativistic Dynamics Without Conservation Postulates. Studia Logica 89 (2):163 - 186.
    A part of relativistic dynamics is axiomatized by simple and purely geometrical axioms formulated within first-order logic. A geometrical proof of the formula connecting relativistic and rest masses of bodies is presented, leading up to a geometric explanation of Einstein’s famous E = mc 2. The connection of our geometrical axioms and the usual axioms on the conservation of mass, momentum and four-momentum is also investigated.
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  5. Hajnal Andréka, István Németi & Tarek Sayed Ahmed (2008). Omitting Types for Finite Variable Fragments and Complete Representations of Algebras. Journal of Symbolic Logic 73 (1):65-89.
    We give a novel application of algebraic logic to first order logic. A new, flexible construction is presented for representable but not completely representable atomic relation and cylindric algebras of dimension n (for finite n > 2) with the additional property that they are one-generated and the set of all n by n atomic matrices forms a cylindric basis. We use this construction to show that the classical Henkin-Orey omitting types theorem fails for the finite variable fragments of first order (...)
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  6. Hajnal Andréka, Judit X. Madarász & István Németi (2005). Mutual Definability Does Not Imply Definitional Equivalence, a Simple Example. Mathematical Logic Quarterly 51 (6):591-597.
    We give two theories, Th1 and Th2, which are explicitly definable over each other , but are not definitionally equivalent. The languages of the two theories are disjoint.
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  7. Steven Givant & Hajnal Andreka (2002). Groups and Algebras of Binary Relations. Bulletin of Symbolic Logic 8 (1):38-64.
    In 1941, Tarski published an abstract, finitely axiomatized version of the theory of binary relations, called the theory of relation algebras, He asked whether every model of his abstract theory could be represented as a concrete algebra of binary relations. He and Jonsson obtained some initial, positive results for special classes of abstract relation algebras. But Lyndon showed, in 1950, that in general the answer to Tarski's question is negative. Monk proved later that the answer remains negative even if one (...)
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  8. Hajnal Andréka, Steven Givant, Szabolcs Mikulás, István Németi & András Simon (1998). Notions of Density That Imply Representability in Algebraic Logic. Annals of Pure and Applied Logic 91 (2-3):93-190.
    Henkin and Tarski proved that an atomic cylindric algebra in which every atom is a rectangle must be representable . This theorem and its analogues for quasi-polyadic algebras with and without equality are formulated in Henkin, Monk and Tarski [13]. We introduce a natural and more general notion of rectangular density that can be applied to arbitrary cylindric and quasi-polyadic algebras, not just atomic ones. We then show that every rectangularly dense cylindric algebra is representable, and we extend this result (...)
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  9. Hajnal Andréka, Robert Goldblatt & István Németi (1998). Relativised Quantification: Some Canonical Varieties of Sequence-Set Algebras. Journal of Symbolic Logic 63 (1):163-184.
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  10. Hajnal Andréka, István Németi & Johan van Benthem (1998). Modal Languages and Bounded Fragments of Predicate Logic. Journal of Philosophical Logic 27 (3):217 - 274.
  11. Hajnal Andréka, István Németi & Johan van Benthem (1998). Modal Languages and Bounded Fragments of Predicate Logic. Journal of Philosophical Logic 27 (3):217-274.
    What precisely are fragments of classical first-order logic showing “modal” behaviour? Perhaps the most influential answer is that of Gabbay 1981, which identifies them with so-called “finite-variable fragments”, using only some fixed finite number of variables (free or bound). This view-point has been endorsed by many authors (cf. van Benthem 1991). We will investigate these fragments, and find that, illuminating and interesting though they are, they lack the required nice behaviour in our sense. (Several new negative results support this claim.) (...)
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  12. Hajnal Andréka (1997). Complexity of Equations Valid in Algebras of Relations Part I: Strong Non-Finitizability. Annals of Pure and Applied Logic 89 (2):149-209.
    We study algebras whose elements are relations, and the operations are natural “manipulations” of relations. This area goes back to 140 years ago to works of De Morgan, Peirce, Schröder . Well known examples of algebras of relations are the varieties RCAn of cylindric algebras of n-ary relations, RPEAn of polyadic equality algebras of n-ary relations, and RRA of binary relations with composition. We prove that any axiomatization, say E, of RCAn has to be very complex in the following sense: (...)
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  13. Hajnal Andréka (1997). Complexity of Equations Valid in Algebras of Relations Part II: Finite Axiomatizations. Annals of Pure and Applied Logic 89 (2-3):211-229.
    We study algebras whose elements are relations, and the operations are natural “manipulations” of relations. This area goes back to 140 years ago to works of De Morgan, Peirce, Schröder . Well known examples of algebras of relations are the varieties RCAn of cylindric algebras of n-ary relations, RPEAn of polyadic equality algebras of n-ary relations, and RRA of binary relations with composition. We prove that any axiomatization, say E, of RCAn has to be very complex in the following sense: (...)
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  14. Hajnal Andréka & Ivo Düntsch (1995). Binary Relations and Permutation Groups. Mathematical Logic Quarterly 41 (2):197-216.
    We discuss some new properties of the natural Galois connection among set relation algebras, permutation groups, and first order logic. In particular, we exhibit infinitely many permutational relation algebras without a Galois closed representation, and we also show that every relation algebra on a set with at most six elements is Galois closed and essentially unique. Thus, we obtain the surprising result that on such sets, logic with three variables is as powerful in expression as full first order logic.
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  15. Hajnal Andréka, Ivo Düntsch & István Németi (1995). Expressibility of Properties of Relations. Journal of Symbolic Logic 60 (3):970-991.
    We investigate in an algebraic setting the question of which logical languages can express the properties integral, permutational, and rigid for algebras of relations.
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  16. Hajnal Andréka, Steven Givant & István Németi (1995). Perfect Extensions and Derived Algebras. Journal of Symbolic Logic 60 (3):775-796.
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  17. Hajnal Andreka, Johan van Benthem & Istvan Nemeti (1995). Back and Forth Between Modal Logic and Classical Logic. Logic Journal of the Igpl 3 (5):685-720.
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  18. Hajnal Andréka, Steven Givant & István Németi (1994). The Lattice of Varieties of Representable Relation Algebras. Journal of Symbolic Logic 59 (2):631-661.
    We shall show that certain natural and interesting intervals in the lattice of varieties of representable relation algebras embed the lattice of all subsets of the natural numbers, and therefore must have a very complicated lattice-theoretic structure.
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  19. Hajnal Andréka & Roger D. Maddux (1994). Representations for Small Relation Algebras. Notre Dame Journal of Formal Logic 35 (4):550-562.
    There are eighteen isomorphism types of finite relation algebras with eight or fewer elements, and all of them are representable. We determine all the cardinalities of sets on which these algebras have representations.
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  20. Hajnal Andréka & Szabolcs Mikulás (1994). Lambek Calculus and its Relational Semantics: Completeness and Incompleteness. [REVIEW] Journal of Logic, Language and Information 3 (1):1-37.
    The problem of whether Lambek Calculus is complete with respect to (w.r.t.) relational semantics, has been raised several times, cf. van Benthem (1989a) and van Benthem (1991). In this paper, we show that the answer is in the affirmative. More precisely, we will prove that that version of the Lambek Calculus which does not use the empty sequence is strongly complete w.r.t. those relational Kripke-models where the set of possible worlds,W, is a transitive binary relation, while that version of the (...)
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  21. Istvan Nemeti & Hajnal Andreka (1994). General Algebraic Logic: A Perspective on “What is Logic”. In Dov M. Gabbay (ed.), What is a Logical System? Oxford University Press
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  22. 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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  23. Hajnal Andréka & István Németi (1979). Not All Representable Cylindric Algebras Are Neat Reducts. Bulletin of the Section of Logic 8 (3):145-147.
  24. Hajnal Andreka, Istvan Nemeti & Ildiko Sain (1979). Program Verification Within and Without Logic. Bulletin of the Section of Logic 8 (3):124-128.
    Theorem 1 states a negative result about the classical semantics j= ! of program schemes. Theorem 2 investigates the reason for this. We conclude that Theorem 2 justies the Henkin-type semantics j= for which the opposite of the present Theorem 1 was proved in [1]{[3] and also in a dierent form in part III of [5]. The strongest positive result on j= is Corollary 6 in [3].
     
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  25. Hajnal Andreka & Istvan Nemeti (1978). Completeness of Floyd Logic. Bulletin of the Section of Logic 7 (3):115-119.
    This is an abstract of our paper \A characterisation of Floyd-provable programs" submitted to Theoretical Computer Science. ! denotes the set of natural numbers. Y =d fyi : i 2 !g is the set of variable symbols. L denotes the set of classical rst order formulas of type t possibly with free variables , where t is the similarity type of arithmetic, i.e. it consists of \+; ; 0; 1" with arities \2; 2; 0; 0".
     
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  26. Hajnal Andréka & István Németi (1978). On Universal Algebraic Logic and Cylindric Algebras. Bulletin of the Section of Logic 7 (4):152-158.