Jónsson term
In universal algebra, within mathematics, a majority term, sometimes called a Jónsson term, is a term t with exactly three free variables that satisfies the equations t(x, x, y) = t(x, y, x) = t(y, x, x) = x.[1]
For example for lattices, the term (x ∧ y) ∨ (y ∧ z) ∨ (z ∧ x) is a Jónsson term.
Sequences of Jónsson term
In general, Jónsson terms, more formally, a sequence of Jónsson terms, is a sequence of ternary terms satisfying certain related idenitities. One of the earliest Maltsev condition, a variety is congruence distributive if and only if it has a sequence of Jónsson terms. [2]
The case of a majority term is given by the special case n=2 of a sequence of Jónsson terms. [3]
Jónsson terms are named after the Icelandic mathematician Bjarni Jónsson.
gollark: You also seem to have said that how stars work is unknown?
gollark: I like unfathomable.
gollark: There was a self replicator built in CGoL some years back. It's hilariously complex and I think involves a universal constructor machine and computer thing.
gollark: They're not exactly his idea. Elementary CAs might be but the original concept is much older.
gollark: Cellular automata are pretty neat but Wolfram seems oddly obsessed with them.
References
- R. Padmanabhan, Axioms for Lattices and Boolean Algebras, World Scientific Publishing Company (2008)
- Originally proved in B. Jónsson, Algebras whose congruence lattices are distributive. Math. Scand., 21:110-121, 1967.
- Clifford Bergman, Universal Algebra: Fundamentals and Selected Topics, Taylor & Francis (2011), p. 124 - 1256
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