It will be great if ArcGIS Desktop/Enterprise could support PostgreSQL 11.
It looks like that was just released in October: PostgreSQL: PostgreSQL 11 Released!
I'm sure we'll get support for it built into upcoming releases and will post back here with a status update when we have an idea about timeframe. I don't believe we'll see it in the Pro 2.3/ArcGIS 10.7 releases which are just around the corner, so hopefully the subsequent one.
Kory, thank you for answer. I wait and see!
Although not yet officially supported, I have successfully used PostgreSQL 11.1 and PostGIS 2.5.1 for the past two months to connect to a spatial database in PostgreSQL from ArcGIS. NOTE: this database was NOT ESRI Enterprise Geodatabase enabled, it is just a plain PostgreSQL / PostGIS database with spatial columns!
I have seen no real issues connecting to such database from ArcMap 10.6.1 and ArcGIS Pro 2.2.4 using both a standard Windows PostgreSQL ODBC DSN and using the "pyodbc" package and arcpy to connect to the database and send SQL DDL statements to create spatial views, and to subsequently acces the created spatial views using a standard ArcGIS Database Connection (*.sde) in the Catalog window to add them to ArcMap or ArcGIS Pro as ArcGIS Query Layers (http://pro.arcgis.com/en/pro-app/help/data/query-layers/what-is-a-query-layer-.htm)
If you have a non-critical (geo)database, and have proper backups, and you are in need of PostgreSQL 11, I think you can give it a try as well to upgrade. Based on my experiences, I think it quite likely you won't run into major issues, but for the official "green light", you'll need to wait for ESRI.
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