Form equivalence class Howard-Rubin Number: 0
Statement:
For any class of similar (universal) algebras \(K\),\(HSP\ K = Mod\ Eq\ K\). (The class of homomorphic images of subalgebras of products of non-empty families of algebras in \(K\) is the same as the class of algebras which satisfy the set of equations holding in every algebra in \(K\).) (The proofs of forms [0 U] and [0 V] in ZF depend on the axiom of regularity.)
Howard-Rubin number: 0 U
Citations (articles):
Andreka/Nemeti [1981]
HSP $K$ is an equational class without the axiom of choice
Connections (notes):
Note [50]
Definitions regarding algebras from Andreka/Nemeta [1981] and Howard/Höft [1981]
References (books):
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