Engineering↗
Identities and Birkhoff's HSP Theorem
Identities, satisfaction, the operators M and Id as a Galois connection, and Birkhoff's HSP theorem identifying varieties with equationally definable classes, with proof.
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Birkhoff
Every page in the KEVOS library tagged Birkhoff. 4 pages.
Engineering↗
Preservation Theorems: Horn, Universal and Positive Sentences
The preservation theorems: Łoś–Tarski for substructures, Lyndon for homomorphisms, Keisler–Galvin for reduced products, Chang–Łoś–Suszko for unions of chains, and their relation…
Engineering↗
Subdirect Products and Birkhoff's Subdirect Representation Theorem
Subdirect products, subdirect irreducibility, the monolith, and Birkhoff's subdirect representation theorem with its Zorn's lemma proof.
Engineering↗
Universal Algebra: Discipline Overview
Structural overview of universal algebra: what an algebra of arbitrary type is, why congruences rather than substructures carry the quotient theory, how Birkhoff's two theorems …
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