Furthermore the dichotomy between elementary and abstract algebra reflects a certain duality in reasoning that Descartes, the inventor of Cartesian Dualism, would have appreciated, wherein the former deals with the reasoning process and the latter that which is reasoned about, as respectively the mind and body of mathematics.
The elementary, but abstract result employed reads as follows: if X is a finite dimensional space with seminorms | · | 1 and | · | 2, an estimate of the type (56) | x | 1 ≤ C | x | 2 for all x ∈ X and some independent constant C > 0 is equivalent to the inclusion (57) { x ∈ X : | x | 2 = 0 } ⊆ { x ∈ X : | x | 1 = 0 } of the respective null spaces.
Sebastien Vasey, Building prime models in fully good abstract elementary classes, Mathematical Logic Quarterly 63 (2017), nos.
Sebastien Vasey, The categoricity spectrum of large abstract elementary classes, Submitted.
Sebastien Vasey, Quasiminimal abstract elementary classes, Archive for Mathematical Logic 57 (2018), nos.
Sebastien Vasey, Saturation and solvability in abstract elementary classes with amalgamation, Archive for Mathematical Logic 56 (2017), nos.
Sebastien Vasey, On the uniqueness property of forking in abstract elementary classes, Mathematical Logic Quarterly 63 (2017), no.
Monica VanDieren and Sebastien Vasey, Symmetry in abstract elementary classes with amalgamation, Archive for Mathematical Logic 56 (2017), no. 3, 423 452.
Sebastien Vasey, Building independence relations in abstract elementary classes, Annals of Pure and Applied Logic 167 (2016), no.
His abstract, elementary forms – often manufactured out of metal tubes like modernist furniture – were meant to belong in a well-mannered streetscape.
Rami Grossberg and Sebastien Vasey, Equivalent definitions of superstability in tame abstract elementary classes, The Journal of Symbolic Logic 82 (2017), no. 4, 1387 1408.
