Heyting Lattices

John Browne-Grassmann Algebra. Exploring extended vector algebra with Mathematica (2009).pdf

@book{book:2116770,
title = {Grassmann Algebra. Exploring extended vector algebra with Mathematica},
author = {John Browne},
publisher = {},
isbn = {},
year = {2009},
series = {},
edition = {Incomplete draft},
volume = {},
url = {http://gen.lib.rus.ec/book/index.php?md5=e95f559406c82c9d547db4bf8fa1872c}
}

Could be good starting text. Excellent appendices.

John Snygg (auth.)-A New Approach to Differential Geometry using Clifford’s Geometric Algebra -Birkhäuser Basel (2012).pdf

@book{book:790059,
title = {A New Approach to Differential Geometry using Clifford’s Geometric Algebra },
author = {John Snygg (auth.)},
publisher = {Birkhäuser Basel},
isbn = {0817682821,9780817682828,9780817682835},
year = {2012},
series = {},
edition = {1},
volume = {},
url = {http://gen.lib.rus.ec/book/index.php?md5=5DD71F6A00D724E868817B7E616C8F38}
}

====move above

https://en.m.wikipedia.org/wiki/Heyting_algebra

https://ncatlab.org/nlab/show/Heyting+algebra

https://en.m.wikipedia.org/wiki/Residuated_lattice

https://en.m.wikipedia.org/wiki/Posetal_category

https://en.m.wikipedia.org/wiki/Complete_Heyting_algebra

https://www.math.upenn.edu/~pjf/Heyting.pdf

On the size of Heyting Semi-Lattices
and Equationally Linear Heyting Algebras ∗
Peter Freyd
pjf@upenn.edu
July 17, 2017

This looks to me a LOT like Robert Grassmann’s “concepts”.

cf relative complement in:

https://en.m.wikipedia.org/wiki/Algebra_of_sets

https://en.m.wikipedia.org/wiki/Field_of_sets

https://en.m.wikipedia.org/wiki/Naive_set_theory

(BTW Check Plato’s Parmenides for possible prefiguring of proof that there is no set of all sets or even more general version for any relation R not exist y s.t. x R y iff x Rx. Ditto for ordinals?)

 

Same Freyd as “categories, allegories”? Yes! Involved in HoTT? (No, not listed at front but 1976 paper cited p239)

(North-Holland Mathematical Library 39) P.J. Freyd, A. Scedrov-Categories, allegories-North Holland (1990).pdf

@book{book:110901,
title = {Categories, allegories},
author = {P.J. Freyd, A. Scedrov},
publisher = {North Holland},
isbn = {9780444703682,0444703683},
year = {1990},
series = {North-Holland Mathematical Library 39},
edition = {1},
volume = {},
url = {http://gen.lib.rus.ec/book/index.php?md5=875566005329DA247F48854629B3F31D}
}

https://www.math.upenn.edu/~pjf/amplifications.pdf

https://www.math.upenn.edu/~pjf/corrections.pdf

 

Algebra univers. 54 (2005) 465–473
0002-5240/05/040465 – 09
DOI 10.1007/s00012-005-1958-5
c Birkh¨auser Verlag, Basel, 2005 Algebra Universalis
Locally finite varieties of Heyting algebras
Guram Bezhanishvili and Revaz Grigolia

Abstract. We show that for a variety V of Heyting algebras the following conditions are
equivalent: (1) V is locally finite; (2) the V-coproduct of any two finite V-algebras is finite;
(3) either V coincides with the variety of Boolean algebras or finite V-copowers of the three
element chain 3 ∈ V are finite. We also show that a variety V of Heyting algebras is
generated by its finite members if, and only if, V is generated by a locally finite V-algebra.
Finally, to the two existing criteria for varieties of Heyting algebras to be finitely generated
we add the following one: V is finitely generated if, and only if, V is residually finite.

http://sierra.nmsu.edu/gbezhani/lfHA.pdf

Computability of Heyting algebras and
Distributive Lattices

Amy Turlington 2010 PhD thesis, U Conn.

http://www.math.uconn.edu/~solomon/Turlingtonthesis.pdf

@article{idziak_idziak_1988, title={Decidability problem for finite Heyting algebras}, volume={53}, DOI={10.2307/2274568}, number={3}, journal={Journal of Symbolic Logic}, publisher={Cambridge University Press}, author={Idziak, Katarzyna and Idziak, Pawel M.}, year={1988}, pages={729–735}}

http://www.math.chapman.edu/~jipsen/structures/doku.php/heyting_algebras

@article{doi:10.1093/jigpal/jzu033,
author = {Alizadeh, Majid and Joharizadeh, Nima},
title = {Counting weak Heyting algebras on finite distributive lattices},
journal = {Logic Journal of the IGPL},
volume = {23},
number = {2},
pages = {247-258},
year = {2015},
doi = {10.1093/jigpal/jzu033},
URL = { + http://dx.doi.org/10.1093/jigpal/jzu033},
eprint = {/oup/backfile/content_public/journal/jigpal/23/2/10.1093/jigpal/jzu033/2/jzu033.pdf}
}

Sheaves and Boolean Valued Model Theory

George Loullis

@article{-,
doi = {10.2307/2273725},
publisher = {Association for Symbolic Logic},
journal = {Journal of Symbolic Logic},
issnp = {0022-4812},
issne = {1943-5886},
year = {},
volume = {44},
issue = {2},
page = {153–183},
url = {http://gen.lib.rus.ec/scimag/index.php?s=10.2307/2273725},
}

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