## Research team

• Martín Moroni
• Mauricio Tellechea (Assistant Professor)
• Pablo Ventura

## Recent Papers (and latest manuscripts)

1. M. A. Campercholi and J. G. Raftery, “Relative congruence formulas and decompositions in quasivarieties,” Algebra universalis (2017).

Quasivarietal analogues of uniform congruence schemes are discussed, and their relationship with the equational definability of principal relative congruences (EDPRC) is established, along with their significance for relative congruences on subalgebras of products. Generalizing the situation in varieties, we prove that a quasivariety is relatively ideal iff it has EDPRC; it is relatively filtral iff it is relatively semisimple with EDPRC. As an application, it is shown that a finitary sentential logic, algebraized by a quasivariety K, has a classical inconsistency lemma if and only if K is relatively filtral and the subalgebras of its nontrivial members are nontrivial. A concrete instance of this result is exhibited, in which K is not a variety. Finally, for quasivarieties {\$}{\$}{\{}{\backslash}sf{\{}M{\}} {\backslash}subseteq {\backslash}sf{\{}K{\}}{\}}{\$}{\$} M ⊆ K , we supply some conditions under which M is the restriction to K of a variety, assuming that K has EDPRC.

@article{Campercholi2017,
author = {Campercholi, Miguel A. and Raftery, James G.},
title = {Relative congruence formulas and decompositions in quasivarieties},
journal = {Algebra universalis},
year = {2017},
month = {Sep},
abstract = {Quasivarietal analogues of uniform congruence schemes are discussed, and their relationship with the equational definability of principal relative congruences (EDPRC) is established, along with their significance for relative congruences on subalgebras of products. Generalizing the situation in varieties, we prove that a quasivariety is relatively ideal iff it has EDPRC; it is relatively filtral iff it is relatively semisimple with EDPRC. As an application, it is shown that a finitary sentential logic, algebraized by a quasivariety K, has a classical inconsistency lemma if and only if K is relatively filtral and the subalgebras of its nontrivial members are nontrivial. A concrete instance of this result is exhibited, in which K is not a variety. Finally, for quasivarieties {\$}{\$}{\{}{\backslash}sf{\{}M{\}} {\backslash}subseteq {\backslash}sf{\{}K{\}}{\}}{\$}{\$} M ⊆ K , we supply some conditions under which M is the restriction to K of a variety, assuming that K has EDPRC.},
day = {27},
doi = {10.1007/s00012-017-0455-y},
issn = {1420-8911},
url = {https://doi.org/10.1007/s00012-017-0455-y}
}

2. M. Badano and D. Vaggione, “Characterization of context-free languages,” Theor. Comput. Sci. 676: 92-96 (2017).
[ BibTeX ]
@article{zbMATH06714282,
author = {M. {Badano} and D. {Vaggione}},
title = {{Characterization of context-free languages}},
fjournal = {{Theoretical Computer Science}},
journal = {{Theor. Comput. Sci.}},
issn = {0304-3975},
volume = {676},
pages = {92--96},
year = {2017},
publisher = {Elsevier, Amsterdam},
language = {English},
doi = {10.1016/j.tcs.2017.03.002},
msc2010 = {68Q}
}

3. M. Badano and D. Vaggione, “$\mathcal{V}_{SI}$ first order implies $\mathcal{V}_{DI}$ first order,” Acta Math. Hung. 151 (1): 47-49 (2017).
[ BibTeX ]
@article{zbMATH06707836,
author = {M. {Badano} and D. {Vaggione}},
title = {{$\mathcal{V}_{SI}$ first order implies $\mathcal{V}_{DI}$ first order}},
fjournal = {{Acta Mathematica Hungarica}},
journal = {{Acta Math. Hung.}},
issn = {0236-5294; 1588-2632/e},
volume = {151},
number = {1},
pages = {47--49},
year = {2017},
language = {English},
doi = {10.1007/s10474-016-0676-0},
msc2010 = {08B10}
}

4. M. V. Badano and D. J. Vaggione, “Varieties with equationally definable factor congruences II,” Algebra Univers. (2017).
[ BibTeX ]
@article{edfc2,
author = {Mariana V. {Badano} and Diego J. {Vaggione}},
title = {{Varieties with equationally definable factor congruences II}},
fjournal = {{Algebra Universalis}},
journal = {{Algebra Univers.}},
issn = {0002-5240; 1420-8911/e},
year = {2017},
publisher = {Springer (Birkh\"auser), Basel; University of Manitoba, Department of Mathematics, Winnipeg},
language = {English},
note = {In press},
msc2010 = {03C05 08B05 08B10}
}