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In a posix-compatible way that works with multiple implementations, how can I print the list of currently defined environment variable without their values?

On some implementations (mksh, freebsd /bin/sh), just using export by itself will fit the bill:

$ export
FOO2
FOO

But for some other implementations (bash, zsh, dash), export also shows the value. With bash, for example:

$ export
export FOO2='as  df\
  asdk=fja:\
asd=fa\
asdf'
export FOO='sjfkasjfd  kjasdf:\
   asdkj=fkajdsf:\
       :askjfkajsf=asdfkj:\
   safdkj'
$ printenv | sed -n l
FOO2=as\tdf\$
  asdk=fja:\$
asd=fa\$
asdf$
FOO=sjfkasjfd  kjasdf:\$
   asdkj=fkajdsf:\$
\t:askjfkajsf=asdfkj:\$
   safdkj$

Other options like env or printenv don't have options to print just the variable names without values, at least not on the linux and freebsd platforms I have tried.

Piping to awk/sed/etc. or trimming the list with parameter expansion techniques (e.g., ${foo%%*=}) is acceptable, but it has to work with values that may span lines and have = and whitespace in the value (see example above).

Answers specific to particular shell implementations are interesting, but I am primarily looking for something that is compatible across implementations.

In a posix-compatible way that works with multiple implementations, how can I print the list of currently defined environment variable without their values?

On some implementations (mksh, freebsd /bin/sh), just using export by itself will fit the bill:

$ export
FOO2
FOO

But for some other implementations (bash, zsh, dash), export also shows the value. With bash, for example:

$ export
export FOO2='as  df\
  asdk=fja:\
asd=fa\
asdf'
export FOO='sjfkasjfd  kjasdf:\
   asdkj=fkajdsf:\
       :askjfkajsf=asdfkj:\
   safdkj'
$ printenv | sed -n l
FOO2=as\tdf\$
  asdk=fja:\$
asd=fa\$
asdf$
FOO=sjfkasjfd  kjasdf:\$
   asdkj=fkajdsf:\$
\t:askjfkajsf=asdfkj:\$
   safdkj$

Other options like env or printenv don't have options to print just the variable names without values, at least not on the linux and freebsd platforms I have tried.

Piping to awk/sed/etc. or trimming the list with parameter expansion techniques (e.g., ${foo%%=*}) is acceptable, but it has to work with values that may span lines and have = and whitespace in the value (see example above).

Answers specific to particular shell implementations are interesting, but I am primarily looking for something that is compatible across implementations.