Lawless order |
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| Authors: | W Charles Holland Alan H Mekler Saharon Shelah |
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| Institution: | (1) Simon Fraser University, V5A 1S6 Burnaby, British Columbia, Canada;(2) Bowling Green State University, 43403 Bowling Green, OH, USA;(3) Simon Fraser University, V5A 1S6 Burnaby, British Columbia, Canada;(4) The Hebrew University, Jerusalem, Israel |
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| Abstract: | R. Baer asked whether the group operation of every (totally) ordered group can be redefined, keeping the same ordered set, so that the resulting structure is an Abelian ordered group. The answer is no. We construct an ordered set (G,  ) which carries an ordered group (G,  , ) but which islawless in the following sense. If (G, *, ) is an ordered group on the same carrier (G, ), then the group (G, *) satisfies no nontrivial equational law.Research partially supported by NSERC of Canada Grants #A4044 and A3040.Research partially supported by NSERC of Canada Grant #U0075.Research partially supported by a grant from the BSF. |
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| Keywords: | Primary 06F15 06A05 secondary 03E99 |
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