The Vorkosigan Saga by Lois McMaster Bujold is set in the far future. Is it ever established exactly when in the future most of the books take place?
Captain Vorpatril's Alliance has this infodump in it:
Barrayar had one of the most bizarre colonization histories in the whole of the Nexus, which was full of the relicts and results of audacious human ventures. The story extended far back to the 23rd Century CE, when wormhole travel had first been developed, launching a human diaspora from Old Earth. A prize because of its breathable atmosphere, the planet drew an early settlement attempt of some fifty thousand would-be colonists. Who promptly disappeared from all contact when their sole wormhole link proved unstable, collapsing with catastrophic results. Missing, presumed dead, and over the next six centuries, all but forgotten.
Till, little more than a hundred years ago, a new jump route was prospected from—to its ultimate regret—Komarr. The explorers discovered a thriving but backward world. Subsequently, twenty years of Komarran-supported Cetagandan occupation had failed to civilize the savage planet, but did succeed in militarizing it.
So the book takes place somewhat more than 700 years after interstellar exploration begins, and that's some time in the 23rd century. ("Somewhat more" because of the amount of time between the beginning of interstellar exploration and the colonization of Barrayar as well as the "little more" tacked onto the hundred years after the end of the Time of Isolation.)
In "Borders of Infinity" (which takes place roughly a decade before Captain Vorpatril's Alliance), Miles tells Suergar that "Today is November 2, '97, Earth Common Era."
Putting all this together, it sounds likely that "Borders of Infinity" takes place in 2997, which would place Miles' birth in 2973. It's also possible that the fudge factors are larger than I think and it's 3073. (No book ever mentions the turn of the millennium; you might think that if it happened when Miles was 27, somebody would have noticed.)
I'm pretty sure Brothers in Arms also has dating evidence that points in a similar direction, in the form of comments about how long stuff in London has been around, but it's vague. I remember convincing myself of the 2973 birth-year on the basis of it at some point before Captain Vorpatril's Alliance came out, but then being unable to find it when I went back later.
5. When did re-vivication technology advance so that some accidental deaths could be "cured"?
LMB) Re-vivication technology -- they're working on it now, y'know. I imagine it was a fairly early development in Miles's timeline; some early version was doubtless up and running by the end of the 22nd Century. Miles is about the 29th or 30th Century. (April 1995)
Another data point is found in "Labyrinth", where Miles thinks of Sun Tzu as having been dead for 4,000 years (it's just before the fight scene). As Sun Tzu is thought to have died around 496 BCE, and Miles probably has no more precise date than we do, that would place the story somewhere around 3500 CE. This is loose, though; Miles is using a multiple of 1,000, and may be rounding off by several centuries.