EQUIVALENTIAL ALGEBRAS VERSUS EQUIVALENTIAL CALCULUS

EQUIVALENTIAL ALGEBRAS VERSUS EQUIVALENTIAL CALCULUS | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 19 February 2026 V1 Latest version Share on EQUIVALENTIAL ALGEBRAS VERSUS EQUIVALENTIAL CALCULUS Author : Alexej P. Pynko 0000-0002-3478-9850 [email protected] Authors Info & Affiliations https://doi.org/10.22541/au.177153217.78403984/v1 78 views 59 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract The key algebraic result of the work is absence of non-two-element sub-directly-irreducibles of the variety of classically equivalential algebras, viz., commutative semigroups with square of their elements being their units, in which case the variety involved is semi-simple and, being congruence-permutable, is congruence-modular as well as is the [quasi-]variety generated by any two-element member, and so is equivalent to the equivalence fragment of the classical logic. As a by-product, we find a natural finite Hilbert-style axiomatization of the latter constituted by the reflexivity, commutativity and multiplicative associativity axioms as well as the Modus Ponens rule. We also show that the variety under consideration, being neither congruence-distributive nor implicative, does not have REDPC. Supplementary Material File (ea-au.pdf) Download 144.22 KB Information & Authors Information Version history V1 Version 1 19 February 2026 Copyright This work is licensed under a Non Exclusive No Reuse License. Keywords algebra calculus logic matrix semi-group Authors Affiliations Alexej P. Pynko 0000-0002-3478-9850 [email protected] Department of Digital Automata Theory (100), V.M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine View all articles by this author Metrics & Citations Metrics Article Usage 78 views 59 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Alexej P. Pynko. EQUIVALENTIAL ALGEBRAS VERSUS EQUIVALENTIAL CALCULUS. Authorea . 19 February 2026. DOI: https://doi.org/10.22541/au.177153217.78403984/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu . Format Please select one from the list RIS (ProCite, Reference Manager) EndNote BibTex Medlars RefWorks Direct import Tips for downloading citations document.getElementById('citMgrHelpLink').addEventListener('click', function() { popupHelp(this.href); return false; }); $(".js__slcInclude").on("change", function(e){ if ($(this).val() == 'refworks') $('#direct').prop("checked", false); $('#direct').prop("disabled", ($(this).val() == 'refworks')); }); View Options View options PDF View PDF Figures Tables Media Share Share Share article link Copy Link Copied! Copying failed. 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