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Journal articles on the topic 'Strongly minimal'

Author: Grafiati

Published: 10 December 2022

Last updated: 25 July 2025

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1

Rao, K. Chandrasekhara, and P. Padma P . Padma. "Strongly Minimal Generalized Boundary." Indian Journal of Applied Research 1, no. 7 (2011): 176–77. http://dx.doi.org/10.15373/2249555x/apr2012/59.

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2

Hrushovski, Ehud, and James Loveys. "Strongly and co-strongly minimal abelian structures." Journal of Symbolic Logic 75, no. 2 (2010): 442–58. http://dx.doi.org/10.2178/jsl/1268917489.

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AbstractWe give several characterizations of weakly minimal abelian structures. In two special cases, dual in a sense to be made explicit below, we give precise structure theorems:1. when the only finite 0-definable subgroup is {0}, or equivalently 0 is the only algebraic element (the co-strongly minimal case);2. when the theory of the structure is strongly minimal.In the first case, we identify the abelian structure as a “near-subspace” A of a vector space V over a division ring D with its induced structure, with possibly some collection of distinguished subgroups of A of finite index in A an

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3

Eleftheriou, Pantelis E., Assaf Hasson, and Ya'acov Peterzil. "Strongly minimal groups in o-minimal structures." Journal of the European Mathematical Society 23, no. 10 (2021): 3351–418. http://dx.doi.org/10.4171/jems/1095.

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4

Hillman, Jonathan A. "Strongly minimal PD4-complexes." Topology and its Applications 156, no. 8 (2009): 1565–77. http://dx.doi.org/10.1016/j.topol.2009.01.006.

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5

Hasson, Assaf, and Ehud Hrushovski. "DMP in strongly minimal sets." Journal of Symbolic Logic 72, no. 3 (2007): 1019–30. http://dx.doi.org/10.2178/jsl/1191333853.

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AbstractWe construct a strongly minimal set which is not a finite cover of one with DMP. We also show that for a strongly minimal theory T, generic automorphisms exist iff T has DMP, thus proving a conjecture of Kikyo and Pillay.

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6

Blossier, Thomas, and Elisabeth Bouscaren. "Finitely axiomatizable strongly minimal groups." Journal of Symbolic Logic 75, no. 1 (2012): 25–50. http://dx.doi.org/10.2178/jsl/1264433908.

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7

Hrushovski, Ehud. "A new strongly minimal set." Annals of Pure and Applied Logic 62, no. 2 (1993): 147–66. http://dx.doi.org/10.1016/0168-0072(93)90171-9.

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8

Hong, Chan Yong, and Tai Keun Kwak. "On minimal strongly prime ideals." Communications in Algebra 28, no. 10 (2000): 4867–78. http://dx.doi.org/10.1080/00927870008827127.

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9

Sun, Weihua, Yuming Xu, and Ning Li. "On minimal strongly KC-spaces." Czechoslovak Mathematical Journal 59, no. 2 (2009): 305–16. http://dx.doi.org/10.1007/s10587-009-0022-6.

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10

Ravi, O., S. Jeyashri, and K. Vijayalakshmi. "On Strongly Minimal \(g\)-Continuous Functions in Minimal Structures." Journal of Advanced Studies in Topology 1, no. 2 (2010): 29. http://dx.doi.org/10.20454/jast.2010.212.

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11

Andrews, Uri, and Julia Knight. "Strongly minimal theories with recursive models." Journal of the European Mathematical Society 20, no. 7 (2018): 1561–94. http://dx.doi.org/10.4171/jems/793.

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12

Chisholm, J., J. F. Knight, and S. Miller. "Computable embeddings and strongly minimal theories." Journal of Symbolic Logic 72, no. 3 (2007): 1031–40. http://dx.doi.org/10.2178/jsl/1191333854.

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AbstractHere we prove that if T and T′ are strongly minimal theories, where T′ satisfies a certain property related to triviality and T does not, and T′ is model complete, then there is no computable embedding of Mod(T) into Mod(T′). Using this, we answer a question from [4], showing that there is no computable embedding of VS into ZS, where VS is the class of infinite vector spaces over ℚ, and ZS is the class of models of Th(ℤ, S). Similarly, we show that there is no computable embedding of ACF into ZS, where ACF is the class of algebraically closed fields of characteristic 0.

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13

Andrews, Uri, Steffen Lempp, and Noah Schweber. "Building models of strongly minimal theories." Advances in Mathematics 386 (August 2021): 107802. http://dx.doi.org/10.1016/j.aim.2021.107802.

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14

L'Innocente, Sonia, Vera Puninskaya, and Carlo Toffalori. "Strongly Minimal Modules Over Group Rings." Communications in Algebra 33, no. 7 (2005): 2089–107. http://dx.doi.org/10.1081/agb-200063504.

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15

Castle, Benjamin, and Assaf Hasson. "Very ampleness in strongly minimal sets." Model Theory 3, no. 2 (2024): 213–58. http://dx.doi.org/10.2140/mt.2024.3.213.

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16

Hillman, Jonathan A. "PD4-complexes with strongly minimal models." Topology and its Applications 153, no. 14 (2006): 2413–24. http://dx.doi.org/10.1016/j.topol.2005.09.002.

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17

Holland, Kitty L. "Strongly minimal fusions of vector spaces." Annals of Pure and Applied Logic 83, no. 1 (1997): 1–22. http://dx.doi.org/10.1016/0168-0072(95)00006-2.

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18

KOWALSKI, PIOTR, and SERGE RANDRIAMBOLOLONA. "STRONGLY MINIMAL REDUCTS OF VALUED FIELDS." Journal of Symbolic Logic 81, no. 2 (2016): 510–23. http://dx.doi.org/10.1017/jsl.2015.61.

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AbstractWe prove that if a strongly minimal nonlocally modular reduct of an algebraically closed valued field of characteristic 0 contains +, then this reduct is bi-interpretable with the underlying field.

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19

Zil'ber, B. I. "Strongly minimal countably categorical theories. III." Siberian Mathematical Journal 25, no. 4 (1985): 559–71. http://dx.doi.org/10.1007/bf00968893.

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20

Zil'ber, B. I. "Strongly minimal countably categorical theories. II." Siberian Mathematical Journal 25, no. 3 (1985): 396–412. http://dx.doi.org/10.1007/bf00968979.

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21

Baronti, M., and G. Lewicki. "Strongly Unique Minimal Projections on Hyperplanes." Journal of Approximation Theory 78, no. 1 (1994): 1–18. http://dx.doi.org/10.1006/jath.1994.1056.

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22

DeVilbiss, Matthew, and James Freitag. "Generic differential equations are strongly minimal." Compositio Mathematica 159, no. 7 (2023): 1387–412. http://dx.doi.org/10.1112/s0010437x23007212.

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In this paper we develop a new technique for showing that a nonlinear algebraic differential equation is strongly minimal based on the recently developed notion of the degree of non-minimality of Freitag and Moosa. Our techniques are sufficient to show that generic order $h$ differential equations with non-constant coefficients are strongly minimal, answering a question of Poizat (1980).

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23

Kulpeshov, B. Sh, In I. Pavlyuk, and S. V. Sudoplatov. "Pseudo-strongly-minimal Structures and Theories." Lobachevskii Journal of Mathematics 45, no. 12 (2024): 6515–25. https://doi.org/10.1134/s199508022460626x.

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24

Ikeda, Koichiro. "Minimal but not strongly minimal structures with arbitrary finite dimensions." Journal of Symbolic Logic 66, no. 1 (2001): 117–26. http://dx.doi.org/10.2307/2694913.

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AbstractAn infinite structure is said to be minimal if each of its definable subset is finite or cofinite. Modifying Hrushovski's method we construct minimal, non strongly minimal structures with arbitrary finite dimensions. This answers negatively to a problem posed by B. I Zilber.

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25

Hasson, Assaf, та Piotr Kowalski. "Strongly minimal expansions of (ℂ, +) definable in o-minimal fields". Proceedings of the London Mathematical Society 97, № 1 (2008): 117–54. http://dx.doi.org/10.1112/plms/pdm052.

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26

Marker, David. "Non Σn axiomatizable almost strongly minimal theories". Journal of Symbolic Logic 54, № 3 (1989): 921–27. http://dx.doi.org/10.2307/2274752.

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Recall that a theory is said to be almost strongly minimal if in every model every element is in the algebraic closure of a strongly minimal set. In 1970 Hodges and Macintyre conjectured that there is a natural number n such that every ℵ0-categorical almost strongly minimal theory is Σn axiomatizable. Recently Ahlbrandt and Baldwin [A-B] proved that if T is ℵ0-categorical and almost strongly minimal, then T is Σn axiomatizable for some n. This result also follows from Ahlbrandt and Ziegler's results on quasifinite axiomatizability [A-Z]. In this paper we will refute Hodges and Macintyre's conj

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27

Anastasoaei, Vasile, and Elefterie Olaru. "New Results on Minimal Strongly Imperfect Graphs." Scientific Annals of Computer Science XVIII (June 5, 2008): 1–12. https://doi.org/10.5281/zenodo.12719793.

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The characterization of strongly perfect graphs by a restricted list of forbidden induced subgraphs has remained an open question for a long time. The minimal strongly imperfect graphs which are simultaneous imperfect are only odd holes and odd antiholes (E. Olaru, 1996), but the entire list is not known, in spite of a lot of particular results in this direction. In this paper we give some new properties of the minimal strongly imperfect graphs. Thus we introduce the notion of critical (co-critical) pair of vertices, and we prove that any vertex of a minimal s-imperfect (minimal c-imperfect) g

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28

Marker, David. "A strongly minimal expansion of (ω, s)". Journal of Symbolic Logic 52, № 1 (1987): 205–7. http://dx.doi.org/10.2307/2273874.

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We will show that there is a nontrivial strongly minimal expansion of (ω, s), the natural numbers with successor. Pillay and Steinhorn [1] proved that there is no -minimal expansion of (ω, ≤). This result provides an interesting contrast.The strongly minimal expansion of (ω, s) is very easy to describe. Consider the order-two permutation of ω, π recursively defined byLet T be Th(ω, s, π, 0).

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29

Blossier, Thomas. "Automorphism groups of trivial strongly minimal structures." Journal of Symbolic Logic 68, no. 2 (2003): 644–68. http://dx.doi.org/10.2178/jsl/1052669069.

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AbstractWe study automorphism groups of trivial strongly minimal structures. First we give a characterization of structures of bounded valency through their groups of automorphisms. Then we characterize the triplets of groups which can be realized as the automorphism group of a non algebraic component, the subgroup stabilizer of a point and the subgroup of strong automorphisms in a trivial strongly minimal structure, and also we give a reconstruction result. Finally, using HNN extensions we show that any profinite group can be realized as the stabilizer of a point in a strongly minimal structu

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30

Buechler, Steven. "Pseudoprojective strongly minimal sets are locally projective." Journal of Symbolic Logic 56, no. 4 (1991): 1184–94. http://dx.doi.org/10.2307/2275467.

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AbstractLet D be a strongly minimal set in the language L, and D′ ⊃ D an elementary extension with infinite dimension over D. Add to L a unary predicate symbol D and let T′ be the theory of the structure (D′, D), where D interprets the predicate D. It is known that T′ is ω-stable. We proveTheorem A. If D is not locally modular, then T′ has Morley rank ω.We say that a strongly minimal set D is pseudoprojective if it is nontrivial and there is a k < ω such that, for all a, b ∈ D and closed X ⊂ D, a ∈ cl(Xb) ⇒ there is a Y ⊂ X with a ∈ cl(Yb) and ∣Y∣ ≤ k. Using Theorem A, we proveTheorem B. If

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31

Puninskaya, V. A. "Strongly minimal modules over right distributive rings." Algebra and Logic 35, no. 3 (1996): 196–203. http://dx.doi.org/10.1007/bf02367218.

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32

Hrushovski, Ehud. "Strongly minimal expansions of algebraically closed fields." Israel Journal of Mathematics 79, no. 2-3 (1992): 129–51. http://dx.doi.org/10.1007/bf02808211.

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33

Kulpeshov, B. Sh, and Ye K. Netaliyeva. "STRONGLY MINIMAL PARTIAL ORDERINGS OF HEIGHT TWO." Herald of the Kazakh-British technical university 22, no. 1 (2025): 223–28. https://doi.org/10.55452/1998-6688-2025-22-1-223-228.

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In the present paper, we study strongly minimal partial orderings in the signature containing only the symbol of binary relation of partial order. We use for partial orderings such characteristics as the height of a structure that is the supremum of lengths of ordered chains, and the width of a structure that is the supremum of lengths of antichains, where an antichain is a set of pairwise incomparable elements. We also differ trivial width and non-trivial width. Recently, B.Sh. Kulpeshov, In.I. Pavlyuk and S.V. Sudoplatov described strongly minimal partial orderings having a finite non-trivia

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34

Marker, David. "Omitting types in -minimal theories." Journal of Symbolic Logic 51, no. 1 (1986): 63–74. http://dx.doi.org/10.2307/2273943.

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Let L be a first order language containing a binary relation symbol <.Definition. Suppose ℳ is an L-structure and < is a total ordering of the domain of ℳ. ℳ is ordered minimal (-minimal) if and only if any parametrically definable X ⊆ ℳ can be represented as a finite union of points and intervals with endpoints in ℳ.In any ordered structure every finite union of points and intervals is definable. Thus the -minimal structures are the ones with no unnecessary definable sets. If T is a complete L-theory we say that T is strongly (-minimal if and only if every model of T is -minimal.The the

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35

Lee, Heakyung. "Strongly right FBN rings." Bulletin of the Australian Mathematical Society 38, no. 3 (1988): 457–64. http://dx.doi.org/10.1017/s0004972700027842.

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The annihilator of a finite generated β-critical module is called a β-coprimative ideal. A prime ideal P is called β-prime if the Krull dimension of R/P is β. This paper is concerned with the relationship between the set of β-prime ideals and the set of minimal β-coprimitive ideals over a strongly right FBN ring. it is shown that there exists a one-to-one correspondence between the set of β-prime ideals and the set on minimal β-coprimitive ideals over a strongly right FBN ring R for −1 < β ≤ α, where α is the Krull dimension of R.

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36

Chudnovsky, Maria, Cemil Dibek, and Paul Seymour. "New examples of minimal non-strongly-perfect graphs." Discrete Mathematics 344, no. 5 (2021): 112334. http://dx.doi.org/10.1016/j.disc.2021.112334.

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37

Holland, Kitty L. "Model completeness of the new strongly minimal sets." Journal of Symbolic Logic 64, no. 3 (1999): 946–62. http://dx.doi.org/10.2307/2586613.

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Boris Zil'ber conjectured that all strongly minimal theories are bi-interpretable with one of the “classical” sorts: theories of algebraically closed fields, theories of infinite vector spaces over division rings and theories with trivial algebraic closure relations. Hrushovski produced the first two classes of counterexample to this conjecture in [10] and [9]. Subsequently, in [8], the author gave an explicit axiomatization of a special case of [9] from which model completeness could quickly be deduced. It was unclear at that writing whether the model completeness result was true in the gener

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38

Moosa, Rahim, та Anand Pillay. "$ℵ_{0}$-categorical strongly minimal compact complex manifolds". Proceedings of the American Mathematical Society 140, № 5 (2012): 1785–801. http://dx.doi.org/10.1090/s0002-9939-2011-11028-1.

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39

Baldwin, John T. "An almost strongly minimal non-Desarguesian projective plane." Transactions of the American Mathematical Society 342, no. 2 (1994): 695–711. http://dx.doi.org/10.1090/s0002-9947-1994-1165085-8.

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40

Serrano, Alberto Castellón, Antonio Fernández López, Amable García Martín, and Cándido Martín González. "Strongly prime alternative pairs with minimal inner ideals." Manuscripta Mathematica 90, no. 1 (1996): 479–87. http://dx.doi.org/10.1007/bf02568320.

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41

Lewicki, Grzegorz, and Agnieszka Micek. "Equality of two strongly unique minimal projection constants." Journal of Approximation Theory 162, no. 12 (2010): 2278–89. http://dx.doi.org/10.1016/j.jat.2010.07.014.

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42

Khachiyan, Leonid, Endre Boros, Khaled Elbassioni, and Vladimir Gurvich. "On Enumerating Minimal Dicuts and Strongly Connected Subgraphs." Algorithmica 50, no. 1 (2007): 159–72. http://dx.doi.org/10.1007/s00453-007-9074-x.

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43

HYTTINEN, TAPANI. "INTERPRETING GROUPS INSIDE MODULAR STRONGLY MINIMAL HOMOGENEOUS MODELS." Journal of Mathematical Logic 03, no. 01 (2003): 127–42. http://dx.doi.org/10.1142/s0219061303000200.

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A large homogeneous (not necessarily saturated) model M is strongly minimal, if any definable subset is either bounded or has bounded complement. In this case (M, bcl) is a pregeometry, where bcl denotes the bounded closure operation. In this paper, we show that if M is a large homogeneous strongly minimal structure and (M, bcl) is non-trivial and locally modular, then M interprets a group. In addition, we give a description of such groups.

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44

Harbrecht, Helmut, Wolfgang L. Wendland, and Natalia Zorii. "Minimal energy problems for strongly singular Riesz kernels." Mathematische Nachrichten 291, no. 1 (2017): 55–85. http://dx.doi.org/10.1002/mana.201600024.

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45

Ziegler, Martin. "An exposition of Hrushovskiʼs New Strongly Minimal Set". Annals of Pure and Applied Logic 164, № 12 (2013): 1507–19. http://dx.doi.org/10.1016/j.apal.2013.06.020.

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46

Kalimoldayev, M. N., A. T. Nurtazin, and Z. G. Khisamiyev. "TWO PROPERTIES OF EXISTENTIALLY CLOSED COMPANIONS OF STRONGLY MINIMAL STRUCTURES." PHYSICO-MATHEMATICAL SERIES 5, no. 333 (2020): 28–32. http://dx.doi.org/10.32014/2020.2518-1726.79.

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The proposed article studies some properties of existentially closed companions of strongly minimal structures. A criterion for the existential closedness of an arbitrary strongly minimal structure is found in the article and it is proved that the existentially closed companion of any strongly minimal structure is itself strongly minimal. It also follows from the resulting description that all existentially closed companions of a given strongly minimal structure form an axiomatizable class whose elementary theory is complete and model-complete and, therefore, coincides with its inductive and f

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47

Xue, Weimin. "Structure of minimal noncommutative duo rings and minimal strongly bounded non-duo rings." Communications in Algebra 20, no. 9 (1992): 2777–88. http://dx.doi.org/10.1080/00927879208824488.

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48

Şahi̇n, Mesut, and Leah Gold Stella. "Gluing semigroups and strongly indispensable free resolutions." International Journal of Algebra and Computation 29, no. 02 (2019): 263–78. http://dx.doi.org/10.1142/s0218196719500012.

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We study strong indispensability of minimal free resolutions of semigroup rings focusing on the operation of gluing used in the literature to take examples with a special property and produce new ones. We give a naive condition to determine whether gluing of two semigroup rings has a strongly indispensable minimal free resolution. As applications, we determine simple gluings of [Formula: see text]-generated non-symmetric, [Formula: see text]-generated symmetric and pseudo symmetric numerical semigroups as well as obtain infinitely many new complete intersection semigroups of any embedding dime

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49

Buechler, Steven. "One theorem of Zil′ber's on strongly minimal sets." Journal of Symbolic Logic 50, no. 4 (1985): 1054–61. http://dx.doi.org/10.2307/2273990.

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AbstractSuppose D ⊂ M is a strongly minimal set definable in M with parameters from C. We say D is locally modular if for all X, Y ⊂ D, with X = acl(X ∪ C)∩D, Y = acl(Y ∪ C) ∩ D and X ∩ Y ≠ ∅,We prove the following theorems.Theorem 1. Suppose M is stable and D ⊂ M is strongly minimal. If D is not locally modular then inMeqthere is a definable pseudoplane.(For a discussion of Meq see [M, §A].) This is the main part of Theorem 1 of [Z2] and the trichotomy theorem of [Z3].Theorem 2. Suppose M is stable and D, D′ ⊂ M are strongly minimal and nonorthogonal. Then D is locally modular if and only if

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50

Dalud-Vincent, Monique. "Minimal closed subsets and strongly connected components in pretopology." Applied Mathematical Sciences 15, no. 6 (2021): 265–81. http://dx.doi.org/10.12988/ams.2021.914485.

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