Dialectics of Mathematics

Alain Badiou, A.J. Bartlett, Alex Ling-Mathematics of the Transcendental_ Onto-logy and being-there-Bloomsbury Academic (2014).pdf

title = {Mathematics of the Transcendental: Onto-logy and being-there},
author = {Alain Badiou, A.J. Bartlett, Alex Ling},
publisher = {Bloomsbury Academic},
isbn = {1441189246,9781441189240},
year = {2014},
series = {},
edition = {},
volume = {},
url = {http://gen.lib.rus.ec/book/index.php?md5=E347ABBF0FFF299BE2F293F15AD124A8}}

Alain Badiou references


@article{higgs_1970, title={Boolean-valued equivalence relations and complete extensions of complete boolean algebras}, volume={3}, DOI={10.1017/S0004972700045652}, number={1}, journal={Bulletin of the Australian Mathematical Society}, publisher={Cambridge University Press}, author={Higgs, Denis}, year={1970}, pages={65–72}}

A catalogue of combinatorial geometries

Authors: John E. Blackburn, Henry H. Crapo and Denis A. Higgs
Journal: Math. Comp. 27 (1973), 155-166
MSC: Primary 05B35
DOI: https://doi.org/10.1090/S0025-5718-1973-0419270-0
MathSciNet review: 0419270
Full-text PDF Free Access

title = "A category-theoretic approach to boolean-valued models of set theory",
journal = "Journal of Pure and Applied Algebra",
volume = "42",
number = "3",
pages = "245 - 274",
year = "1986",
issn = "0022-4049",
doi = "https://doi.org/10.1016/0022-4049(86)90010-1",
url = "http://www.sciencedirect.com/science/article/pii/0022404986900101",
author = "G.P. Monro",
abstract = "Abstract Let B be a complete Boolean algebra. Scott and Solovay constructed a B-valued model of set theory V(B); in this paper a category-theoretic translation of V(B) is given, in the form of a B-valued model of category theory. The usual category-theoetic translation of V(B), namely the category of sheaves Shv(B), appears as an image of the B-valued model. The B-valued model lives in a category MOD(B), which is intended to be the category of all B-valued models. The last part of the paper investigates Easton's construction, which is the construction of V(B) for a ‘large’ B. The construction (in MOD(B)) of the B-valued model of category theory can still be carried out in this case, though the construction of Shv(B) fails."
@article{loullis_1979, title={Sheaves and Boolean valued model theory}, volume={44}, DOI={10.2307/2273725}, number={2}, journal={Journal of Symbolic Logic}, publisher={Cambridge University Press}, author={Loullis, George}, year={1979}, pages={153–183}}

Injectivity in the topos of complete Heyting algebra valued sets

Canad. J. Math. 36(1984), 550-568
Denis Higgs

title = {Sheaves in geometry and logic: a first introduction to topos theory},
author = {Saunders MacLane, Ieke Moerdijk},
publisher = {Springer},
isbn = {9780387977102,0387977104},
year = {1994},
series = {Universitext},
edition = {Corrected},
volume = {},
url = {http://gen.lib.rus.ec/book/index.php?md5=D9767DA02739F77571B8FAC78C374D53}

See also Lattice Valued Models

(move most of above)


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