View More View Less
  • 1 Department of Mathematics, Faculty of Science, Cairo University
Restricted access

Purchase article

USD  $25.00

1 year subscription (Individual Only)

USD  $800.00

Abstract

Fix 2 < n < ω and let CAn denote the class of cyindric algebras of dimension n. Roughly CAn is the algebraic counterpart of the proof theory of first order logic restricted to the first n variables which we denote by Ln. The variety RCAn of representable CAns reflects algebraically the semantics of Ln. Members of RCAn are concrete algebras consisting of genuine n-ary relations, with set theoretic operations induced by the nature of relations, such as projections referred to as cylindrifications. Although CAn has a finite equational axiomatization, RCAn is not finitely axiomatizable, and it generally exhibits wild, often unpredictable and unruly behavior. This makes the theory of CAn substantially richer than that of Boolean algebras, just as much as Lω,ω is richer than propositional logic. We show using a so-called blow up and blur construction that several varieties (in fact infinitely many) containing and including the variety RCAn are not atom-canonical. A variety V of Boolean algebras with operators is atom canonical, if whenever 𝔄 V is atomic, then its Dedekind-MacNeille completion, sometimes referred to as its minimal completion, is also in V. From our hitherto obtained algebraic results we show, employing the powerful machinery of algebraic logic, that the celebrated Henkin-Orey omitting types theorem, which is one of the classical first (historically) cornerstones of model theory of Lω,ω, fails dramatically for Ln even if we allow certain generalized models that are only locallly clasfsical. It is also shown that any class K such that NrnCAωCRCAn¯K¯ScNrnCAn+3 , where CRCAn is the class of completely representable CAns, and Sc denotes the operation of forming dense (complete) subalgebras, is not elementary. Finally, we show that any class K such that SdRaCAω¯K¯ScRaCA5 is not elementary, where Sd denotes the operation of forming dense subalgebra.

  • [1]

    Sayed Ahmed, T., The class of completely representable polyadic algebras of infinite dimensions is elementary, Algebra universalis, 72(1) (2014), 371390.

    • Search Google Scholar
    • Export Citation
  • [2]

    Andréka, H., Complexity of equations valid in algebras of relations. Annals of Pure and Applied Logic 89(1997), 149209.

  • [3]

    Andréka, H., Finite axiomatizability of SNrnCAn+1 and non–finite axiomatizability of SNrnCAn+2, Lecture notes, Algebraic Logic Meeting, Oakland, CA (1990).

    • Search Google Scholar
    • Export Citation
  • [4]

    Andréka, H., Ferenczi, M. and NÉMETI, I., (Editors), Cylindric-like Algebras and Algebraic Logic, Bolyai Society Mathematical Studies 22, 2013.

    • Search Google Scholar
    • Export Citation
  • [5]

    Andréka, H., Németi, I. and Sayed Ahmed, T., Omitting types for finite variable fragments and complete representations, Journal of Symbolic Logic, 73 (2008), 6589.

    • Search Google Scholar
    • Export Citation
  • [6]

    Biró, B., Non-finite axiomatizability results in algebraic logic, Journal of Symbolic Logic, 57(3) (1992), 832843.

  • [7]

    Bulian, J. and Hodkinson, I., Bare canonicity of representable cylindric and polyadic algebras, Annals of Pure and Applied Logic, 164 (2013), 884906.

    • Search Google Scholar
    • Export Citation
  • [8]

    Blackburn, P., DE Rijke, M. and Venema, Y., Modal logic, Cambridge University Press (2001).

  • [9]

    Daigneault, A. and Monk, J. D., Representation Theory for Polyadic algebras, Fundamenta Mathematica, 52 (1963), 151176 .

  • [10]

    Fremlin, D. H., Consequences of Martin's axiom, Cambridge University Press, 1984.

  • [11]

    Henkin, L., Monk, J. D. and Tarski, A., Cylindric Algebras, Paris I, II, North Holland, 1971 .

  • [12]

    Hirsch, R., Relation algebra reducts of cylindric algebras and complete representations, Journal of Symbolic Logic, 72(2) (2007), 673703.

    • Search Google Scholar
    • Export Citation
  • [13]

    Hirsch, R., Corrigendum to 'Relation algebra reducts of cylindric algebras and complete representations', Journal of Symbolic Logic, 78(4) (2013), 13451348.

    • Search Google Scholar
    • Export Citation
  • [14]

    Hirsch, R. and Hodkinson, I., Complete representations in algebraic logic, Journal of Symbolic Logic, 62(3) (1997) 816847 .

  • [15]

    Hirsch, R. and Hodkinson, I., Relation algebras by games, Studies in Logic and the Foundations of Mathematics, 147 (2002 ).

  • [16]

    Hirsch, R. and Hodkinson, I., Strongly representable atom structures of cylindic algebras ,Journal of Symbolic Logic, 74 (2009), 811828 .

    • Search Google Scholar
    • Export Citation
  • [17]

    Hirsch, R. and Hodkinson, I., Completions and complete representations , in: Andréka, H., Ferenczi, M. and Németi, I., (Editors),Cylindric-like Algebras and, Algebraic Logic, Bolyai Society Mathematical Studies 22, 6190, 2013 .

    • Search Google Scholar
    • Export Citation
  • [18]

    Hirsch, R. and Sayed Ahmed, T., The neat embedding problem for algebras other than cylindric algebras and for infinite dimensions, Journal of Symbolic Logic, 79(1) (2014), 208222.

    • Search Google Scholar
    • Export Citation
  • [19]

    Hodkinson, I., Atom structures of relation and cylindric algebras, Annals of pure and applied logic, 89 (1997), 117148 .

  • [20]

    Johnson, J. S., Nonfinitizability of classes of Polyadic Algebras, Journal of Symbolic Logic, 34(3) (1969), 344352.

  • [21]

    Khaled, M. and Sayed Ahmed, T., On complete representations of algebrs of logic, IGPL, 17 (2009), 267272.

  • [22]

    Maddux, R., Non finite axiomatizability results for cylindric and relation algebras, Journal of Symbolic Logic, (1989) 54, 951974 .

  • [23]

    Monk, J. D., Non finitizability of classes of representable cylindric algebras, Journal of Symbolic Logic, 34 (1969), 331343 .

  • [24]

    Németi, I. and Sági, G., On the equational theory of Representable Polyadic Algebras, Journal of Symbolic Logic, 65(3) (2000), 1143-1167.

    • Search Google Scholar
    • Export Citation
  • [25]

    Pinter, C., Cylindric algebras and algebras of substitutions, Transactions of the American Mathematical Society, 175 (1973), 167-179 .

  • [26]

    Sági, G., Non computability of the Equational Theory of Polyadic Algebras, Bulletin of the Section of Logic, 3 (2001), 155-165.

  • [27]

    Sain, I. and Thompson, R., Strictly finite schema axiomatization of quasi-polyadic algebras. in: Algebraic Logic, North Holland, Editors Andréka,H., Monk, D., and Németi, I., 539572.

    • Search Google Scholar
    • Export Citation
  • [28]

    Sayed Ahmed, T., The class of neat reducts is not elementary, Logic Journal of IGPL, 9 (2001), 593628.

  • [29]

    Sayed Ahmed, T., The class of 2-dimensional polyadic algebras is not elementary, Fundamenta Mathematica, 172 (2002), 6181 .

  • [30]

    Sayed Ahmed, T., A note on neat reducts, Studia Logica, 85 (2007), 139151.

  • [31]

    Sayed Ahmed, T., A model-theoretic solution to a problem of Tarski, Math Logic Quarterly, 48 (2002), 343355.

  • [32]

    Sayed Ahmed, T., RaCAn is not elementary for n ≥5, Bulletin Section of Logic, 37(2) (2008), 123136.

  • [33]

    Sayed Ahmed, T., Completions, Complete representations and Omitting types , in: Andréka, H., Ferenczi, M. and Németi, I., (Editors), Cylindric-like Algebras and Algebraic Logic, Bolyai Society Mathematical Studies 22, 186205, 2013.

    • Search Google Scholar
    • Export Citation
  • [34]

    Sayed Ahmed, T., Neat reducts and neat embeddings in cylindric algebras , in: Andréka, H., Ferenczi, M. and Németi, I., (Editors),Cylindric-like Algebras and, Algebraic Logic, Bolyai Society Mathematical Studies 22, 105-134, 2013.

    • Search Google Scholar
    • Export Citation
  • [35]

    Sayed Ahmed, T., On notions of representability for cylindric–polyadic algebras and a solution to the finitizability problem for first order logic with equality, Mathematical Logic Quarterly, 61(6) (2015), 418447.

    • Search Google Scholar
    • Export Citation
  • [36]

    Sayed Ahmed, T., Notions of Representability for cylindric and polyadic algebras, Studia Mathematicea Hungarica ,56(3) (2019), 335-363.

  • [37]

    Sayed Ahmed, T. and Németi, I., On neat reducts of algebras of logic, Studia Logica, 68(2) (2001), 229262.

  • [38]

    Sayed Ahmed, T. and Samir, B., Omitting types for first order logic with infini- tary predicates, Mathematical Logic Quaterly, 53(6) (2007) 564576.

    • Search Google Scholar
    • Export Citation
  • [39]

    Shelah, S., Classification theory: and the number of non-isomorphic models, Studies in Logic and the Foundations of Mathematics (1990 ).

  • [40]

    Venema, Y., Cylindric modal Logic in: Andréka, H., Ferenczi, M. and Németi, I.,(Editors), Cylindric-like Algebras and Algebraic Logic, Bolyai Society Mathematical Studies 22, 2013.

    • Search Google Scholar
    • Export Citation
  • [41]

    Venema, Y., Atom structures and Sahlqvist equations, Algebra Universalis, 38(1997), 185199.

Editors in Chief

Gábor SIMONYI (Rényi Institute of Mathematics)
András STIPSICZ (Rényi Institute of Mathematics)
Géza TÓTH (Rényi Institute of Mathematics) 

Managing Editor

Gábor SÁGI (Rényi Institute of Mathematics)

Editorial Board

  • Imre BÁRÁNY (Rényi Institute of Mathematics)
  • Károly BÖRÖCZKY (Rényi Institute of Mathematics and Central European University)
  • Péter CSIKVÁRI (ELTE, Budapest) 
  • Joshua GREENE (Boston College)
  • Penny HAXELL (University of Waterloo)
  • Andreas HOLMSEN (Korea Advanced Institute of Science and Technology)
  • Ron HOLZMAN (Technion, Haifa)
  • Satoru IWATA (University of Tokyo)
  • Tibor JORDÁN (ELTE, Budapest)
  • Roy MESHULAM (Technion, Haifa)
  • Frédéric MEUNIER (École des Ponts ParisTech)
  • Márton NASZÓDI (ELTE, Budapest)
  • Eran NEVO (Hebrew University of Jerusalem)
  • János PACH (Rényi Institute of Mathematics)
  • Péter Pál PACH (BME, Budapest)
  • Andrew SUK (University of California, San Diego)
  • Zoltán SZABÓ (Princeton University)
  • Martin TANCER (Charles University, Prague)
  • Gábor TARDOS (Rényi Institute of Mathematics)
  • Paul WOLLAN (University of Rome "La Sapienza")

STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA
Gábor Sági
Address: P.O. Box 127, H–1364 Budapest, Hungary
Phone: (36 1) 483 8344 ---- Fax: (36 1) 483 8333
E-mail: smh.studia@renyi.mta.hu

Indexing and Abstracting Services:

  • CompuMath Citation Index
  • Essential Science Indicators
  • Mathematical Reviews
  • Science Citation Index Expanded (SciSearch)
  • SCOPUS
  • Zentralblatt MATH
2020  
Total Cites 536
WoS
Journal
Impact Factor
0,855
Rank by Mathematics 189/330 (Q3)
Impact Factor  
Impact Factor 0,826
without
Journal Self Cites
5 Year 1,703
Impact Factor
Journal  0,68
Citation Indicator  
Rank by Journal  Mathematics 230/470 (Q2)
Citation Indicator   
Citable 32
Items
Total 32
Articles
Total 0
Reviews
Scimago 24
H-index
Scimago 0,307
Journal Rank
Scimago Mathematics (miscellaneous) Q3
Quartile Score  
Scopus 139/130=1,1
Scite Score  
Scopus General Mathematics 204/378 (Q3)
Scite Score Rank  
Scopus 1,069
SNIP  
Days from  85
sumbission  
to acceptance  
Days from  123
acceptance  
to publication  
Acceptance 16%
Rate

2019  
Total Cites
WoS
463
Impact Factor 0,468
Impact Factor
without
Journal Self Cites
0,468
5 Year
Impact Factor
0,413
Immediacy
Index
0,135
Citable
Items
37
Total
Articles
37
Total
Reviews
0
Cited
Half-Life
21,4
Citing
Half-Life
15,5
Eigenfactor
Score
0,00039
Article Influence
Score
0,196
% Articles
in
Citable Items
100,00
Normalized
Eigenfactor
0,04841
Average
IF
Percentile
13,117
Scimago
H-index
23
Scimago
Journal Rank
0,234
Scopus
Scite Score
76/104=0,7
Scopus
Scite Score Rank
General Mathematics 247/368 (Q3)
Scopus
SNIP
0,671
Acceptance
Rate
14%

 

Studia Scientiarum Mathematicarum Hungarica
Publication Model Hybrid
Submission Fee none
Article Processing Charge 900 EUR/article
Printed Color Illustrations 40 EUR (or 10 000 HUF) + VAT / piece
Regional discounts on country of the funding agency World Bank Lower-middle-income economies: 50%
World Bank Low-income economies: 100%
Further Discounts Editorial Board / Advisory Board members: 50%
Corresponding authors, affiliated to an EISZ member institution subscribing to the journal package of Akadémiai Kiadó: 100%
Subscription Information Online subsscription: 672 EUR / 840 USD
Print + online subscription: 760 EUR / 948 USD
Online subscribers are entitled access to all back issues published by Akadémiai Kiadó for each title for the duration of the subscription, as well as Online First content for the subscribed content.
Purchase per Title Individual articles are sold on the displayed price.

Studia Scientiarum Mathematicarum Hungarica
Language English
French
German
Size B5
Year of
Foundation
1966
Publication
Programme
2021 Volume 58
Volumes
per Year
1
Issues
per Year
4
Founder Magyar Tudományos Akadémia
Founder's
Address
H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Publisher's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Responsible
Publisher
Chief Executive Officer, Akadémiai Kiadó
ISSN 0081-6906 (Print)
ISSN 1588-2896 (Online)