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Thompson's group $F$ is totally ordered. See here for a description of all possible bi-orderings. Indeed, all diagram groups are totally orderable (see here). The pure braided Thompson group $BF$ also bi-orderable (see here).

Thompson's group $F$ is totally ordered. See here for a description of all possible bi-orderings. Indeed, all diagram groups are totally orderable (see here). The pure braided Thompson group $BF$ also bi-orderable (see here).

Thompson's group $F$ is totally ordered. See here for a description of all possible bi-orderings. Indeed, all diagram groups are totally orderable (see here). The pure braided Thompson group $BF$ also bi-orderable (see here).

Thompson's group $F$ is totally ordered. See here for a description of all possible bi-orderings. Indeed, all diagram groups are totally orderable (see here). The pure braided Thompson group $BF$ also bi-orderable (see here).

Thompson's group $F$ is totally ordered. See here for a description of all possible bi-orderings. Indeed, all diagrams groups are totally orderable (see here). The pure braided Thompson group $BF$ also bi-orderable (see here).

Thompson's group $F$ is totally ordered. See here for a description of all possible bi-orderings. Indeed, all diagram groups are totally orderable (see here). The pure braided Thompson group $BF$ also bi-orderable (see here).