“…As said in the introduction, strong standard completeness of a logic L can be shown by proving that any countable L-chain is embeddable into a standard Lchain, and that it can be achieved by densification and a subsequent MacNeille completion. Involutive Uninorm Logic with Fixed Point (IUL f p ) has been introduced in [16], we refer the reader to the introduction of [9] for a motivation for this interesting logic. Knowing that IUL fp -chains, that is, non-trivial bounded odd involutive FL e -chains constitute an algebraic semantics of IUL f p , we shall prove in this paper that any non-trivial countable, bounded odd involutive FL e -chain embeds into an odd involutive FL e -chain over the real unit interval [0, 1] such that its top element is mapped into 1 and its bottom element is mapped into 0.…”