We introduce a concept of implication groupoid which is an essential generalization of the implication reduct of intuitionistic logic, i.e. a Hilbert algebra. We prove several connections among ideals, deductive systems and congruence kernels which even coincide whenever our implication groupoid is distributive.
@article{bwmeta1.element.doi-10_2478_s11533-007-0021-5,
author = {Ivan Chajda and Radomir Hala\v s},
title = {Distributive implication groupoids},
journal = {Open Mathematics},
volume = {5},
year = {2007},
pages = {484-492},
zbl = {1134.03042},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-007-0021-5}
}
Ivan Chajda; Radomir Halaš. Distributive implication groupoids. Open Mathematics, Tome 5 (2007) pp. 484-492. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-007-0021-5/
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