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The first part is that Hetman Khmelnytsky continues his attack on Poland through the election King Jon II so as to not lose momentum. Then perhaps defeating and/or capturing the King as he was almost captured at the battle of Zbroriv, except earlier on, and farther west. Would Poland actually accept defeat if the King was captured or killed? Would the Moldavians contribute the Cossack effort? Could the Muscovites be convinced to join in an anti-polish alliance, but on equal terms instead of OTL's? Considering the more advantageous position of Hetman Khmelnytsky's forces? Would it be necessary to hold back a Polish attempt at re conquest? Could Sweden join in against Poland so soon after the end of the thirty years war?

The second important part is that perhaps the Tartars can be convinced to stay on the Ukrainian/Cossack side until one or two crucial victories that see Hetman Khmelnytsky able to safely declare independence from Poland-Lithuania. Or delay their switching sides until the Cossacks are strong enough and the Poles weak enough where it won't cost the Cossacks the war.

Assuming the Cossacks defeat the Polish-Lithuanian Commonwealth by say 1651, and have an alliance with Muscovy and/or Moldavia what would the Hetmanate do? I assume Hetman Khmelnytsky would try to turn it into a hereditary monarchy based in Kyiv with himself as Grand Prince and Hetman. I imagine peace with the Tartars would be impossible and Poland would try to reconquer Ukraine. However with Sweden or Muscovy as allies I think the Cossack/Kyivan state would be able to survive until at least the late 18th century.
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