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Wikipedia states:

"there may exist many homomorphisms from a Boolean algebra B to 2".

I would be very grateful for any references to the literature that there always exists a homomorphism from B to the 2-element Boolean algebra $\mathbf2$.

Victor M
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    Fix an ultrafilter $U$ of $B$. Define $f:B\to \mathbf 2$ by $f(x)=1$ iff $x \in U$. – amrsa Jun 17 '23 at 17:04
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    Except if $B$ is trivial, i.e., $|B|=1$. In that case, you can only define homomorphisms from $B$ to other trivial Boolean algebras (which are then isomorphisms). – amrsa Jun 17 '23 at 17:11
  • @amrsa Thank you, And references to the literature? – Victor M Jun 17 '23 at 19:35
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    I guess most books on Boolean algebra make some reference to that simple result. Do you have difficulties in understanding why does it work? It may be helpful to know that in Boolean algebras, ultrafilters are the same thing as prime filters. – amrsa Jun 17 '23 at 19:45
  • https://mathoverflow.net/questions/449096/unquantified-theorems-preserved-under-a-homomorphism-from-a-power-set-boolean-al – Victor M Jun 17 '23 at 21:58
  • @amrsa Thanks again.I also just asked a related question on MathOverflow:https://mathoverflow.net/questions/449096/unquantified-theorems-preserved-under-a-homomorphism-from-a-power-set-boolean-al – Victor M Jun 17 '23 at 22:08

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