Volodyrmyr Yelchenko was right: Statesmen as diverse as Henry Kissinger and Mikhail Gorbachev have taken up the cause of "nuclear abolition." And this year's U.S. presidential contenders both support a more favorable American stance toward arms control.
But other forces are pushing back. Renewed interest in nuclear energy, to stem global warming, is expected to give more states the technological building blocks for a bomb. The continuing revelations about the Pakistani scientist A.Q. Khan's network, which reportedly had blueprints for a compact weapon, show that globalized nuclear smuggling is growing more sophisticated and dangerous.
As much as anything, the perpetuation of the exclusive club of "accepted" nuclear powers - from old hands America and Russia to newest members India and Pakistan - may lead others, frustrated with such a two-tier world, to consider challenging the doomsday cartel.
Even if North Korea follows through on Friday's destruction of the cooling tower at its Yongbyon complex and fully dismantles its weapons program, giving up its handful of bombs, it will still belong to another club of nuclear-capable states.
Those are the 40-plus countries with the scientists, engineers and infrastructure for building bombs - and in at least one other case, that of South Africa, a history of having done so.
About a dozen are nuclear "rollback" states, ranging from Sweden and Switzerland, which seriously researched the weapon option in the 1950s and 1960s and then pulled back, to Iraq under Saddam Hussein, which desperately tried, and failed, to produce a bomb before the 1991 Gulf war.
Rebecca Hersman, a proliferation expert at Washington's National Defense University, stresses that nuclear rollback is "a process, not an outcome." Those who have been there before could go that way again.
"Success in the past by no means assures success in the future," Hersman says. The dominoes could fall the other way.
Success in the future, the specialists say, depends heavily on success in "rolling back" North Korea and Iran, which is accused by Washington and others of clandestinely planning a bomb. Iran denies that, saying its atomic program is aimed at using nuclear reactors to generate electricity.
If North Korea balks at final disarmament, if Iran moves toward an atomic arsenal despite international pressure, some of their neighbors may reconsider the nuclear option.
South Korea, still technically at war with the north, had a secret nuclear weapons program it abandoned in the 1970s, under U.S. pressure. Hersman says its first-rate nuclear-power industry today puts Seoul in an excellent position to quickly build a bomb if it feels threatened.
Across the Sea of Japan, in the only nation to have suffered atomic bombings, the possibility of a made-in-Japan bomb was a taboo subject for a half-century. In recent years, however, as the North Korean threat loomed larger, Tokyo's leadership has spoken more openly of that option. Its leading-edge nuclear establishment is well equipped for it.
Taiwan, another Asian "rollback" state, launched a secret weapons program in the 1970s, as it watched U.S.-China relations thaw and feared losing its American nuclear shield. By the late 1980s, under U.S. pressure, it ended its flirtation with the ultimate weapon, but it's believed capable of quickly reviving the program if tensions heighten with nuclear-armed China.
In step with Iran's year-by-year advances in uranium enrichment, a process key to both nuclear power and bomb-making, Saudi Arabia and Tehran's other Arab rivals across the Persian Gulf have plunged into planning for nuclear power, with French and U.S. help. The Arabs' Gulf Cooperation Council has proposed its own regional uranium-enrichment operation.
In Egypt, last January's announcement of plans for its first nuclear power plant could signal something of a "bounceback" four decades after nationalist President Gamal Abdel Nasser briefly explored the idea of nuclear arms.
Those who monitor such developments don't predict rapidly falling dominoes - an impending "breakout" of new weapons states. Robert J. Einhorn, a former U.S. government arms-control specialist, notes that over the past 40 years more nations abandoned weapons programs than initiated them.
Instead, other countries may follow "rollback" state Brazil's example, positioning themselves as compliant with the Nonproliferation Treaty's ban on bombs, but equipping themselves with the power technology - enrichment centrifuges - that enable them "to move rapidly to weaponization if and when needed," as Einhorn says.
For some, near-nuclear may be near enough.