API search for observations without field

Is there a way to use the API v1 to return only observations which do not have a particular Observation Field? (I’m interested only in doing this via the API, not via a generalized filter.)

see https://forum.inaturalist.org/t/filter-for-without-field-fieldname/6652/20

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Thank you @pisum!
I didn’t realize that would work with the API.
@tiwane: It would be great to add this (and field=) to the API1 documentation.