On Complete Representations and Minimal Completions in Algebraic Logic, Both Positive and Negative Results

Tarek Sayed Ahmed

Bulletin of the Section of Logic (2021)

  • Volume: 50, Issue: 4, page 465-511
  • ISSN: 0138-0680

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Tarek Sayed Ahmed. "On Complete Representations and Minimal Completions in Algebraic Logic, Both Positive and Negative Results." Bulletin of the Section of Logic 50.4 (2021): 465-511. <http://eudml.org/doc/298964>.

@article{TarekSayedAhmed2021,
author = {Tarek Sayed Ahmed},
journal = {Bulletin of the Section of Logic},
keywords = {Algebraic logic; relation algebras; cylindric algebras; polyadic algebras; complete representations},
number = {4},
pages = {465-511},
title = {On Complete Representations and Minimal Completions in Algebraic Logic, Both Positive and Negative Results},
url = {http://eudml.org/doc/298964},
volume = {50},
year = {2021},
}

TY - JOUR
AU - Tarek Sayed Ahmed
TI - On Complete Representations and Minimal Completions in Algebraic Logic, Both Positive and Negative Results
JO - Bulletin of the Section of Logic
PY - 2021
VL - 50
IS - 4
SP - 465
EP - 511
KW - Algebraic logic; relation algebras; cylindric algebras; polyadic algebras; complete representations
UR - http://eudml.org/doc/298964
ER -

References

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  13. R. Hirsch, T. Sayed Ahmed, The neat embedding problem for algebras other than cylindric algebras and for infinite dimensions, The Journal of Symbolic Logic, vol. 79(1) (2014), pp. 208–222, DOI: https://doi.org/10.1017/jsl.2013.20 
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  17. T. Sayed Ahmed, The class of neat reducts is not elementary, Logic Journal of the IGPL, vol. 9(4) (2001), pp. 593–628, DOI: https://doi.org/10.1093/jigpal/9.4.593 
  18. T. Sayed Ahmed, The class of 2-dimensional neat reducts is not elementary, Fundamenta Mathematicae, vol. 172 (2002), pp. 61–81, DOI: https://doi.org/10.4064/fm172-1-5 
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  20. T. Sayed Ahmed, Algebraic Logic, Where Does it Stand Today?, Bulletin of Symbolic Logic, vol. 11(4) (2005), pp. 465–516, DOI: https://doi.org/10.2178/bsl/1130335206 
  21. T. Sayed Ahmed, A Note on Neat Reducts, Studia Logica: An International Journal for Symbolic Logic, vol. 85(2) (2007), pp. 139–151, DOI: https://doi.org/10.2307/40210764 
  22. T. Sayed Ahmed, (RaCA_n) is not elementary for (ngeq 5), Bulletin of the Section of Logic, vol. 37(2) (2008), pp. 123–136. 
  23. T. Sayed Ahmed, Atom-canonicity, relativized representations and omitting types for clique guarded semantics and guarded logics (2013), arXiv:1308.6165. 
  24. T. Sayed Ahmed, Completions, Complete Representations and Omitting Types, [in:] H. Andréka, M. Ferenczi, I. Németi (eds.), Cylindric-like Algebras and Algebraic Logic, Springer Berlin Heidelberg, Berlin, Heidelberg (2013), pp. 205–221, DOI: https://doi.org/10.1007/978-3-642-35025-2_10 
  25. T. Sayed Ahmed, Neat Reducts and Neat Embeddings in Cylindric Algebras, [in:] H. Andréka, M. Ferenczi, I. Németi (eds.), Cylindric-like Algebras and Algebraic Logic, Springer Berlin Heidelberg, Berlin, Heidelberg (2013), pp. 105–131, DOI: https://doi.org/10.1007/978-3-642-35025-2_6 
  26. T. Sayed Ahmed, The class of completely representable polyadic algebras of infinite dimensions is elementary, Algebra Universalis, vol. 72(4) (2014), pp. 371–380, DOI: https://doi.org/10.1007/s00012-014-0307-y 
  27. T. Sayed Ahmed, On notions of representability for cylindric‐polyadic algebras, and a solution to the finitizability problem for quantifier logics with equality, Mathematical Logic Quarterly, vol. 61(6) (2015), pp. 418–477, DOI: https://doi.org/10.1002/malq.201300064 
  28. T. Sayed Ahmed, Splitting methods in algebraic logic: Proving results on non-atom-canonicity, non-finite axiomatizability and non-first oder definability for cylindric and relation algebras (2015), arXiv:1503.02189. 
  29. T. Sayed Ahmed, Atom-canonicity in algebraic logic in connection to omitting types in modal fragments of (L_{omega, omega}) (2016), arXiV:1608.03513. 

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