On Complete Representations and Minimal Completions in Algebraic Logic, Both Positive and Negative Results
Bulletin of the Section of Logic (2021)
- Volume: 50, Issue: 4, page 465-511
- ISSN: 0138-0680
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topTarek 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
top- H. Andréka, M. Ferenczi, I. Németi (eds.), Cylindric-like Algebras and Algebraic Logic, Springer Berlin Heidelberg, Berlin, Heidelberg (2013), DOI: https://doi.org/10.1007/978-3-642-35025-2_1
- H. Andréka, I. Németi, T. S. Ahmed, Omitting types for finite variable fragments and complete representations of algebras, Journal of Symbolic Logic, vol. 73(1) (2008), pp. 65–89, DOI: https://doi.org/10.2178/jsl/1208358743
- A. Daigneault, J. Monk, Representation Theory for Polyadic algebras, Fundamenta Informaticae, vol. 52 (1963), pp. 151–176, DOI: https://doi.org/10.4064/fm-52-2-151-176
- M. Ferenczi, The Polyadic Generalization of the Boolean Axiomatization of Fields of Sets, Transactions of the American Mathematical Society, vol. 364(2) (2012), pp. 867–886, DOI: https://doi.org/10.2307/41407800
- M. Ferenczi, A New Representation Theory: Representing Cylindric-like Algebras by Relativized Set Algebras, [in:] H. Andréka, M. Ferenczi, I. Németi (eds.), Cylindric-like Algebras and Algebraic Logic, Springer Berlin Heidelberg, Berlin, Heidelberg (2013), pp. 135–162, DOI: https://doi.org/10.1007/978-3-642-35025-2_7
- M. Ferenczi, Representations of polyadic-like equality algebras, Algebra Universalis, vol. 75(1) (2016), pp. 107–125, DOI: https://doi.org/10.1007/s00012-015-0360-1
- L. Henkin, J. Monk, A. Tarski, Cylindric Algebras Parts I, II, North Holland, Amsterdam (1971).
- R. Hirsch, Relation algebra reducts of cylindric algebras and complete representations, Journal of Symbolic Logic, vol. 72(2) (2007), pp. 673–703, DOI: https://doi.org/10.2178/jsl/1185803629
- R. Hirsch, I. Hodkinson, Complete representations in algebraic logic, Journal of Symbolic Logic, vol. 62(3) (1997), pp. 816–847, DOI: https://doi.org/10.2307/2275574
- R. Hirsch, I. Hodkinson, Relation algebras by games, vol. 147 of Studies in Logic and the Foundations of Mathematics, North Holland, Amsterdam (2002).
- R. Hirsch, I. Hodkinson, Completions and Complete Representations, [in:] H. Andréka, M. Ferenczi, I. Németi (eds.), Cylindric-like Algebras and Algebraic Logic, Springer Berlin Heidelberg, Berlin, Heidelberg (2013), pp. 61–89, DOI: https://doi.org/10.1007/978-3-642-35025-2_4
- R. Hirsch, I. Hodkinson, R. D. Maddux, Relation algebra reducts of cylindric algebras and an application to proof theory, Journal of Symbolic Logic, vol. 67(1) (2002), pp. 197–213, DOI: https://doi.org/10.2178/jsl/1190150037
- 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
- I. Hodkinson, Atom structures of cylindric algebras and relation algebras, Annals of Pure and Applied Logic, vol. 89(2) (1997), pp. 117–148, DOI: https://doi.org/10.1016/S0168-0072(97)00015-8
- J. S. Johnson, Nonfinitizability of classes of representable polyadic algebras, Journal of Symbolic Logic, vol. 34(3) (1969), pp. 344–352, DOI: https://doi.org/10.2307/2270901
- R. D. Maddux, Nonfinite axiomatizability results for cylindric and relation algebras, Journal of Symbolic Logic, vol. 54(3) (1989), pp. 951–974, DOI: https://doi.org/10.2307/2274756
- 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
- 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
- T. Sayed Ahmed, A Modeltheoretic Solution to a Problem of Tarski, Mathematical Logic Quarterly, vol. 48(3) (2002), pp. 343–355, DOI: https://doi.org/10.1002/1521-3870(200204)48:3<343::AID-MALQ343>3.0.CO;2-4
- 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
- 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
- T. Sayed Ahmed, (RaCA_n) is not elementary for (ngeq 5), Bulletin of the Section of Logic, vol. 37(2) (2008), pp. 123–136.
- T. Sayed Ahmed, Atom-canonicity, relativized representations and omitting types for clique guarded semantics and guarded logics (2013), arXiv:1308.6165.
- 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
- 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
- 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
- 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
- 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.
- 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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