Set Theory and Logic


Refutation of a 'concrete' Rauszer Boolean Algebra Generated by a Preorder

Authors: Colin James III

From the 11 equations tested, we refute 13 artifacts: 1. a condition for "an existential quantifier ∃ … on a Boolean algebra"; 2. "a quantifier ∃ as closure operator on B, for which every open element is closed"; 3. the interior operator on abstract topological Boolean algebra; 4. the kernel of a homomorphism from a Heyting algebra into another as a filter; 5. deductive systems and filters as equivalent; 6. the atomic definition of p ≤ ∃p in Halmos algebra; 7. a ‘concrete’ Rauszer Boolean algebra; 8. two conditions for the definition of a filter (and Heyting algebra using the filter); 9. a De Morgan algebra as a Kleene algebra; 10. equivalences of symmetrical Heyting algebras; 11. equivalences in Heyting algebras; 12. intuitionistic implication of intuitionistic logic; and 13. a theorem and a proposition of Nelson algebras. As a result, the following seven areas are non tautologous fragments of the universal logic VŁ4: 1. Topological Boolean algebra; 2. Heyting algebra; 3. Intuitionistic logic; 4. Halmos algebra; 5. Rauszer algebra; 6. Kleene algebra; and 7. Nelson algebra.

Comments: 5 Pages. © Copyright 2019 by Colin James III All rights reserved. Respond to author by email only: info@cec-services dot com. See updated abstract at

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Submission history

[v1] 2019-05-27 21:13:09

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