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2. Complexity in the interdefinability of timelike, lightlike and spacelike relatedness of Minkowski spacetime

Author

Andréka, Hajnal, Madarász, Judit X., Németi, István, and Székely, Gergely

Subjects
Mathematics - Logic
Abstract

Interdefinability of timelike, lightlike and spacelike relatedness of Minkowski spacetime is investigated in detail in the paper, with the aim of finding the simplest definitions. Based on ideas scattered in the literature, definitions are given between any two of these relations that use only 4 variables. All these definitions work over arbitrary Euclidean fields in place of the field of reals, if the dimension n of spacetime is greater than two. If n=2, the definitions work over arbitrary ordered fields except the ones based on lightlike relatedness (where no definition can work by symmetry). None of these relations can be defined from another one using only 3 variables. Our four-variable definitions use only one universal and one existential quantifiers in a specific order. In some of the cases, we show that the order of these quantifiers can be reversed for the price of using twice as many quantifiers. Except two cases, we provide existential/universal definitions using 5 variables or show that no existential/universal definition exists. There are no existential/universal definitions between any two of these relations using only 4 variables. It remains open whether there is an existential (universal) definition of timelike (lightlike) relatedness from spacelike relatedness if $n>2$. Finally, several other open problems related to the quantifier complexity of the simplest possible definitions are given., Comment: 30 pages, 18 figures, 3 tables

Published
2021
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3. Generalizations and new kinds of logics

Author

Andréka, Hajnal, Gyenis, Zalán, Németi, István, Sain, Ildikó, Andréka, Hajnal, Editorial Board Member, Beziau, Jean-Yves, Series Editor, Burgin, Mark, Editorial Board Member, Diaconescu, Răzvan, Editorial Board Member, Herzig, Andreas, Editorial Board Member, Koslow, Arnold, Editorial Board Member, Lee, Jui-Lin, Editorial Board Member, Maksimova, Larissa, Editorial Board Member, Malinowski, Grzegorz, Editorial Board Member, Paoli, Francesco, Editorial Board Member, Schröder-Heister, Peter, Editorial Board Member, Vasyukov, Vladimir, Editorial Board Member, Zamansky, Anna, Editorial Board Member, Giovagnoli, Raffaela, Editorial Board Member, Gyenis, Zalán, Németi, István, and Sain, Ildikó

Published
2022
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4. General framework and algebraization

Author

Andréka, Hajnal, Gyenis, Zalán, Németi, István, Sain, Ildikó, Andréka, Hajnal, Editorial Board Member, Beziau, Jean-Yves, Series Editor, Burgin, Mark, Editorial Board Member, Diaconescu, Răzvan, Editorial Board Member, Herzig, Andreas, Editorial Board Member, Koslow, Arnold, Editorial Board Member, Lee, Jui-Lin, Editorial Board Member, Maksimova, Larissa, Editorial Board Member, Malinowski, Grzegorz, Editorial Board Member, Paoli, Francesco, Editorial Board Member, Schröder-Heister, Peter, Editorial Board Member, Vasyukov, Vladimir, Editorial Board Member, Zamansky, Anna, Editorial Board Member, Giovagnoli, Raffaela, Editorial Board Member, Gyenis, Zalán, Németi, István, and Sain, Ildikó

Published
2022
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5. Appendix: Algebras of relations

Author

Andréka, Hajnal, Gyenis, Zalán, Németi, István, Sain, Ildikó, Andréka, Hajnal, Editorial Board Member, Beziau, Jean-Yves, Series Editor, Burgin, Mark, Editorial Board Member, Diaconescu, Răzvan, Editorial Board Member, Herzig, Andreas, Editorial Board Member, Koslow, Arnold, Editorial Board Member, Lee, Jui-Lin, Editorial Board Member, Maksimova, Larissa, Editorial Board Member, Malinowski, Grzegorz, Editorial Board Member, Paoli, Francesco, Editorial Board Member, Schröder-Heister, Peter, Editorial Board Member, Vasyukov, Vladimir, Editorial Board Member, Zamansky, Anna, Editorial Board Member, Giovagnoli, Raffaela, Editorial Board Member, Gyenis, Zalán, Németi, István, and Sain, Ildikó

Published
2022
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6. Applying the machinery: Examples

Author

Andréka, Hajnal, Gyenis, Zalán, Németi, István, Sain, Ildikó, Andréka, Hajnal, Editorial Board Member, Beziau, Jean-Yves, Series Editor, Burgin, Mark, Editorial Board Member, Diaconescu, Răzvan, Editorial Board Member, Herzig, Andreas, Editorial Board Member, Koslow, Arnold, Editorial Board Member, Lee, Jui-Lin, Editorial Board Member, Maksimova, Larissa, Editorial Board Member, Malinowski, Grzegorz, Editorial Board Member, Paoli, Francesco, Editorial Board Member, Schröder-Heister, Peter, Editorial Board Member, Vasyukov, Vladimir, Editorial Board Member, Zamansky, Anna, Editorial Board Member, Giovagnoli, Raffaela, Editorial Board Member, Gyenis, Zalán, Németi, István, and Sain, Ildikó

Published
2022
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7. Bridge between logic and algebra

Author

Andréka, Hajnal, Gyenis, Zalán, Németi, István, Sain, Ildikó, Andréka, Hajnal, Editorial Board Member, Beziau, Jean-Yves, Series Editor, Burgin, Mark, Editorial Board Member, Diaconescu, Răzvan, Editorial Board Member, Herzig, Andreas, Editorial Board Member, Koslow, Arnold, Editorial Board Member, Lee, Jui-Lin, Editorial Board Member, Maksimova, Larissa, Editorial Board Member, Malinowski, Grzegorz, Editorial Board Member, Paoli, Francesco, Editorial Board Member, Schröder-Heister, Peter, Editorial Board Member, Vasyukov, Vladimir, Editorial Board Member, Zamansky, Anna, Editorial Board Member, Giovagnoli, Raffaela, Editorial Board Member, Gyenis, Zalán, Németi, István, and Sain, Ildikó

Published
2022
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8. Notation, Elementary Concepts

Author

Andréka, Hajnal, Gyenis, Zalán, Németi, István, Sain, Ildikó, Andréka, Hajnal, Editorial Board Member, Beziau, Jean-Yves, Series Editor, Burgin, Mark, Editorial Board Member, Diaconescu, Răzvan, Editorial Board Member, Herzig, Andreas, Editorial Board Member, Koslow, Arnold, Editorial Board Member, Lee, Jui-Lin, Editorial Board Member, Maksimova, Larissa, Editorial Board Member, Malinowski, Grzegorz, Editorial Board Member, Paoli, Francesco, Editorial Board Member, Schröder-Heister, Peter, Editorial Board Member, Vasyukov, Vladimir, Editorial Board Member, Zamansky, Anna, Editorial Board Member, Giovagnoli, Raffaela, Editorial Board Member, Gyenis, Zalán, Németi, István, and Sain, Ildikó

Published
2022
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9. Basics from Universal Algebra

Author

Andréka, Hajnal, Gyenis, Zalán, Németi, István, Sain, Ildikó, Andréka, Hajnal, Editorial Board Member, Beziau, Jean-Yves, Series Editor, Burgin, Mark, Editorial Board Member, Diaconescu, Răzvan, Editorial Board Member, Herzig, Andreas, Editorial Board Member, Koslow, Arnold, Editorial Board Member, Lee, Jui-Lin, Editorial Board Member, Maksimova, Larissa, Editorial Board Member, Malinowski, Grzegorz, Editorial Board Member, Paoli, Francesco, Editorial Board Member, Schröder-Heister, Peter, Editorial Board Member, Vasyukov, Vladimir, Editorial Board Member, Zamansky, Anna, Editorial Board Member, Giovagnoli, Raffaela, Editorial Board Member, Gyenis, Zalán, Németi, István, and Sain, Ildikó

Published
2022
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10. A representation theorem for measurable relation algebras with cyclic groups

Author

Andréka, Hajnal and Givant, Steven

Subjects
Mathematics - Logic, 03G15, 20A15
Abstract

A relation algebra is measurable if the identity element is a sum of atoms, and the square x;1;x of each subidentity atom x is a sum of non-zero functional elements. These functional elements form a group Gx. We prove that a measurable relation algebra in which the groups Gx are all finite and cyclic is completely representable. A structural description of these algebras is also given., Comment: This is the fourth member of a series of papers on measurable relation algebras

Published
2018

11. The variety of coset relation algebras

Author

Givant, Steven and Andréka, Hajnal

Subjects
Mathematics - Logic, 03G15, 03C05, 03C60, 03E20, 20A15, 03C52, 08C10
Abstract

A coset relation algebra is one embeddable into some full coset relation algebra, the latter is an algebra constructed from a system of groups, a coordinated system of isomorphisms between quotients of these groups, and a system of cosets that are used to "shift" the operation of relative multiplication. We prove that the class of coset relation algebras is equationally axiomatizable (that is to say, it is a variety), but no finite set of equations suffices to axiomatize the class (that is to say, the class is not finitely axiomatizable)., Comment: This is the fifth member of a series of papers on measurable relation algebras. Forthcoming in The Journal of Symbolic Logic. arXiv admin note: text overlap with arXiv:1804.00279

Published
2018
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13. An Axiom System for General Relativity Complete with respect to Lorentzian Manifolds

Author

Andréka, Hajnal, Madarász, Judit X., Németi, István, and Székely, Gergely

Subjects
General Relativity and Quantum Cosmology, Mathematics - Logic
Abstract

We introduce several axiom systems for general relativity and show that they are complete with respect to the standard models of general relativity, i.e., to Lorentzian manifolds having the corresponding smoothness properties., Comment: 30 pages, 6 figures

Published
2013

21. Semipowers

Author

Givant, Steven, Andréka, Hajnal, Givant, Steven, and Andréka, Hajnal

Published
2017
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25. A note on 'Einstein's special relativity beyond the speed of light by James M. Hill and Barry J. Cox'

Author

Andréka, Hajnal, Madarász, Judit X., Németi, István, and Székely, Gergely

Subjects
General Relativity and Quantum Cosmology, Mathematical Physics
Abstract

We show that the transformations J. M. Hill and B. J. Cox introduce between inertial observers moving faster than light with respect to each other are consistent with Einstein's principle of relativity only if the spacetime is 2 dimensional., Comment: 7 pages, 3 figures

Published
2012
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26. On Logical Analysis of Relativity Theories

Author

Andréka, Hajnal, Németi, István, Madarász, Judit X., and Székely, Gergely

Subjects
General Relativity and Quantum Cosmology, Mathematical Physics, Mathematics - Logic
Abstract

The aim of this paper is to give an introduction to our axiomatic logical analysis of relativity theories., Comment: 19 pages, 1 figures

Published
2011

27. Closed Timelike Curves in Relativistic Computation

Author

Andréka, Hajnal, Németi, István, and Székely, Gergely

Subjects
General Relativity and Quantum Cosmology, Mathematical Physics, Mathematics - Logic
Abstract

In this paper, we investigate the possibility of using closed timelike curves (CTCs) in relativistic hypercomputation. We introduce a wormhole based hypercomputation scenario which is free from the common worries, such as the blueshift problem. We also discuss the physical reasonability of our scenario, and why we cannot simply ignore the possibility of the existence of spacetimes containing CTCs., Comment: 17 pages, 5 figures

Published
2011
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28. A logic road from special relativity to general relativity

Author

Andréka, Hajnal, Madarász, Judit X., Németi, István, and Székely, Gergely

Subjects
General Relativity and Quantum Cosmology, Mathematical Physics, Mathematics - Logic
Abstract

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.

Published
2010
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30. Visualizing some ideas about Godel-type rotating universes

Author

Nemeti, Istvan, Madarasz, Judit X., Andreka, Hajnal, and Andai, Attila

Subjects
General Relativity and Quantum Cosmology
Abstract

This paper consists mostly of pictures visualizing ideas leading to Godel's rotating cosmological model. The pictures are constructed according to concrete metric tensor fields. Information about these are in the last chapters. The main aim is to visualise ideas., Comment: 84 pages, 70 figures

Published
2008

31. A twist in the geometry of rotating black holes: seeking the cause of acausality

Author

Andreka, Hajnal, Nemeti, Istvan, and Wuthrich, Christian

Subjects
General Relativity and Quantum Cosmology, Physics - History and Philosophy of Physics
Abstract

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 opposite 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 this counter-rotation is not an accidental oddity particular to Kerr-Newman spacetimes, but instead there may be a general and intuitively comprehensible reason for this., Comment: 21 pages, 5 figures; replaced to match published version forthcoming in General Relativity and Gravitation

Published
2007
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36. Introduction

Author

Andréka, Hajnal, Ferenczi, Miklós, Németi, István, Tóth, Gábor Fejes, editor, Miklós, Dezső, editor, Andréka, Hajnal, editor, Ferenczi, Miklós, editor, and Németi, István, editor

Published
2013
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43. Residuated Kleene Algebras

Author

Andréka, Hajnal, Mikulás, Szabolcs, Németi, István, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Constable, Robert L., editor, and Silva, Alexandra, editor

Published
2012
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49. Can General Relativistic Computers Break the Turing Barrier?

Author

Németi, István, Andréka, Hajnal, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Sudan, Madhu, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Dough, Series editor, Vardi, Moshe Y., Series editor, Weikum, Gerhard, Series editor, Beckmann, Arnold, editor, Berger, Ulrich, editor, Löwe, Benedikt, editor, and Tucker, John V., editor

Published
2006
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50. Universal Algebra

Author

Artamonov, Vyacheslav A., Pilz, Günter F., Plotkin, Boris I., Kaarli, Kalle, Shevrin, Lev N., Sukhanov, Evgeny V., Volkov, Mikhail V., Pinus, A. G., Katsov, Yefim, Bokut’, Leonid, Andréka, Hajnal, Madarász, Judit X., Németi, István, Burmeister, Peter, Ehrich, Hans-Dieter, Mikhalev, Alexander V., and Pilz, Günter F.

Published
2002
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