Set Theory and Logic


Refutation of Category Theory by Lattice Identity, and Graph-Theoretic / Set-of-Blocks in Partitions

Authors: Colin James III

We evaluate a definition and two models of a method in graph theory to define any Boolean operation. The definition is not tautologous, refuting that only partition tautologies using only the lattice operations correspond to general lattice-theoretic identities. Defined models of graph-theoretic and set-of-blocks do not produce a common edge, but rather show the graph-theoretic definition implies the set-of-blocks definition. This refutes the graph-theoretic model as defining any Boolean operation on lattice partitions of category theory. What follows is that general lattice theory is also refuted via partitions. Therefore the conjectures form a non tautologous fragment of the universal logic VŁ4.

Comments: 3 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] 2019-06-14 08:34:23

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