@article { author = {Lawvere, F. William}, title = {Birkhoff's Theorem from a geometric perspective: A simple example}, journal = {Categories and General Algebraic Structures with Applications}, volume = {4}, number = {1}, pages = {1-8}, year = {2016}, publisher = {Shahid Beheshti University}, issn = {2345-5853}, eissn = {2345-5861}, doi = {}, abstract = {‎From Hilbert's theorem of zeroes‎, ‎and from Noether's ideal theory‎, ‎Birkhoff derived certain algebraic concepts (as explained by Tholen) that have a dual significance in general toposes‎, ‎similar to their role in the original examples of algebraic geometry‎. ‎I will describe a simple example that illustrates some of the aspects of this relationship‎. The dualization from algebra to geometry in the basic Grothendieck spirit can be accomplished (without intervention of topological spaces) by the following method‎, ‎known as Isbell conjugacy.}, keywords = {Grothendieck spectrum,Cantor,Boole,Hilbert,Birkhoff: Existence and Sufficiency of generalized points,Reflexive Graphs}, url = {https://cgasa.sbu.ac.ir/article_12425.html}, eprint = {https://cgasa.sbu.ac.ir/article_12425_b4ce2ab0ae3a843f00ff011b054f918b.pdf} }