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Three Ultrafilters in a Modular Logic

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Abstract

We have conjectured that the equational theory of the modular logics is completely determined by its finite-dimensional members. Being able to embed an arbitrary modular logic into an atomistic one would almost certainly settle this Conjecture positively. A natural method of embedding a complemented modular lattice into an atomistic one is provided by the Frink embedding. In the case of a modular logic, much of the orthogonality structure can be carried through the embedding as well. Unfortunately, not enough of it to produce a modular logic as the codomain of the resulting ortho-embedding. The main technical result of this paper is an example which proves this.

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Authors and Affiliations

  1. TUD FB4, Schlossgartenstr. 7, 64289, Darmstadt, Germany

    Christian Herrmann

  2. Department of Mathematics and Computer Science, Brandon University, Brandon Mb, R7A 6A9, Canada

    Micheale Susan Roddy

Authors
  1. Christian Herrmann
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  2. Micheale Susan Roddy
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Correspondence to Micheale Susan Roddy.

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Herrmann, C., Roddy, M.S. Three Ultrafilters in a Modular Logic. Int J Theor Phys 50, 3821–3827 (2011). https://doi.org/10.1007/s10773-011-0902-z

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  • DOI: https://doi.org/10.1007/s10773-011-0902-z

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