Timeline for What kind of algebra is the class of ordered pairs equipped with the binary operation which forms them?
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| Jul 13, 2014 at 20:47 | comment | added | Gerhard Paseman | It depends on how you arrange things. The Jonsson-Tarski algebras mentioned in another answer have a nice equational setup: l(p(x,y))=x=r(p(y,x))= p(l(x),r(x)). This gives trivial or infinite algebras, and is a nice example to use in studying algebras with pairing and projection functions. Gerhard "Ask Me About System Design" Paseman, 2014.07.13 | |
| Jul 13, 2014 at 20:32 | comment | added | Ioachim Drugus | It is nice to hear that (*) reduces to quasiidentities. So, these algebras form a quasivariety. This reduction is done via the two projections. Interesting, if we add symbols for projections to the signature of this algebra would the theory of new algebras be essentially the same? It seems I sure ask this manner - "would the theory of new algebras be a conservative extension?" | |
| Jul 13, 2014 at 0:12 | comment | added | Nik Weaver | And therefore the class of sets equipped with a binary operation which satisfies these conditions is stable under isomorphisms, subalgebras, and products. | |
| Jul 12, 2014 at 22:40 | history | answered | Bjørn Kjos-Hanssen | CC BY-SA 3.0 |