Examples:

<field name="my_field" invisible="context.get('default_my_other', False)" />

or

<field name="my_field" attrs="{'invisible': [('field_my_other','=',False)]}" />

Thanks to all of you, especially to Zbik for his 2 links, with which I was able to achieve my goal.   

hey try this

<field name="my_field" attrs="{'column_invisible': [('my_other_field','=',False)]}" />

One solution to completely remove a column from a basic tree view.

    def fields_view_get(self, view_id=None, view_type='tree', toolbar=False, submenu=False):
        result = super(ThisModel, self).fields_view_get(view_id=view_id, view_type=view_type, toolbar=toolbar, submenu=submenu)
        if not self.env.context.get('show_the_column', False) and view_type == 'tree':
            doc = etree.fromstring(result['arch'])
            for field in doc.xpath('//field[@name="name_of_conditional_column"]'):
                field.set('invisible', '1')
                modifiers = json.loads(field.get('modifiers', '{}'))
                modifiers['tree_invisible'] = True
                modifiers['column_invisible'] = True
                field.set('modifiers', json.dumps(modifiers))
            result['arch'] = etree.tostring(doc)
        return result