The SNP leader admitted the word "national" could be "hugely problematic".
Fringe Programme Unveiled
England cricket hero Andrew Flintoff will make his debut at the Edinburgh Fringe this summer, in one of more than 3,300 shows to be staged at the 2015 festival.
The star, nicknamed Freddie, is one of the headline names in the programme's spoken word section.
He will be joined on stage by comedy writer Clyde Holcroft in what is billed as "an unscripted trip down memory lane offering insights into the world of cricket''.
Other well-known names to feature in this year's line-up include House of Commons Speaker John Bercow and actors John Hannah and Ricky Tomlinson, as well as comedy favourites Jo Brand, Ed Byrne, Sue Perkins and Alan Davies.
Overall, this year will see 50,459 performances of 3,314 shows from 49 countries in 313 venues across the Scottish capital.
The number of shows reflects a 3.8% increase on last year's programme, taking the number of performances beyond the 50,000 mark for the first time in its history.
Organisers officially launched the programme today and described it as "innovative, international and adventurous''.
They promise "something for everyone'' with a programme covering theatre, dance, circus, physical theatre, comedy, music, musicals, opera, cabaret and variety, children's shows, free shows, exhibitions, events and the spoken word.
Kath Mainland, chief executive of the Edinburgh Festival Fringe Society, said: "The Edinburgh Festival Fringe is the largest, oldest, most well-renowned festival in the world.
"Every year we think we know what it's going to deliver, but every year it surprises, delights, amazes and inspires.
"The Fringe is a festival like no other. Completely open access - where artists don't need to wait for an invitation, where anyone with a story to tell is welcome. Where there's no curator, no vetting, no barriers. Just incredible talent from almost 50 countries all over the world.
"It's also an incredibly important festival for Scotland, the UK and our performing artists.
"A vital platform to showcase the range and diversity of creative skills on offer. A profoundly international market place which can have transformative effects on careers. An explosion of culture which can be life-changing for the audience. And lots and lots of fun.''
Hollywood and Scottish actor John Hannah will take to the stage as a mysterious illusionist in the UK premiere of Bulgarian play The Titanic Orchestra.
Mr Bercow will discuss his career, the role of the House of Commons Speaker and the future of Westminster in an event at the University of Edinburgh's Business School while Tomlinson is set to deliver a "no holds barred conversation'' about his past before he became an actor.
Under the comedy banner, others bringing their material to the 2015 Fringe include Al Murray, Fred MacAulay, Paul Merton, Marcus Brigstocke and Nina Conti.
Music forms 14% of this year's programme, with a "diverse mix'' of genres for audiences to choose from.
As the Fringe continues to grow, 14 additional new venues will play host to performing companies this year.
Underbelly will introduce Circus Hub on the Meadows in the city's southside, providing a space for what organisers describe as "the most technically ambitious circus performances on a scale the Fringe has never seen before''.
Hit show The Lady Boys of Bangkok will move away from the Meadows to their new location at Fountainbridge alongside the Union Canal.
This year's programme also includes 807 free shows and 1,778 premieres. The Royal Mile and The Mound will once again be a vibrant stage for street entertainers.
Scottish Culture Secretary Fiona Hyslop said: "This year's programme shows once again why the Edinburgh Festival Fringe is one of the most important events in the international cultural calendar.
"The festival is a premier event bringing thousands of people to Scotland. It demonstrates the scale of Scotland's creativity and ambition and raises our standing on the world stage.''
This year's Fringe runs from August 7 to 31.
A police watchdog probe was launched after the remains of the 52-year-old were found in a house in Dumfries in February last year.
The accident happened at about 7.50pm on Thursday in Moodiesburn, North Lanarkshire.
More than 70 firefighters were needed to bring the blaze under control at Blochairn Fruit Market in the early hours of Thursday.
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