Postmodernism, the child of modernism having therefore many of the same characteristics though carried to new extremes in a mood of celebration, is characterized by fragmentation of time and character creating various degrees of disunity and incoherence in the (1) literary structure and in the (2) characters personas and lives, with both categories being marked by ambiguity and a resultant loss of integral meaning.
Some additional specifics of postmodernism, characteristics shared with the parent theory of modernism, are (1) a blurring of or a rejection of the ideas of high and low literary subjects, diction, and themes, which means that the common person and vernacular (or even low persons and vernacular) and the corresponding subject matter and themes are fit for literary immortalization; (2) the prevalence of literary reflexivity, also called self-consciousness, about the literary process, product and intent, in other words, comments within the narrative that indicate a conscious author who is consciously making literary, stylistic, thematic, and narrative choices; (3) the preference for ambiguity, as ambiguity is seen to reflect the discontinuity and disordered nature of life.
In Joyce Carol Oates short story, "The Lady with the Pet Dog," which is a recasting of Chekhov's famous short story translated variously as "The Lady with the Little Dog," "The Lady with the Dog," and "The Lady with the Pet Dog," Oates' structure does depend on a fragmentation of time; the story comes is fits and starts, so to speak, of discontinuity in time. This structure also adheres to the postmodernist ideology of literary aesthetic that turns against traditional aesthetic while embracing an aesthetic that favors a blurring of distinctions and forms.
The central character, Anna, shows some fragmentation of her personality in that she is faced with a feeling of loss of self and confusing choices, with further fragmentation demonstrated through her suicidal intents. Another point demonstrating postmodernism in the story is that Anna's epiphany and the story resolution embody ambiguity in that moral order is upturned and Anna devises her own ideology and moral stance in a world and life that had otherwise lost unity and meaning.