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I have been given a slightly different definition than usually found in Set theory literature.

Namely, in my lecture notes for any ordinal $\delta$, we define $\delta^+$ to be the smallest cardinal which is $>\delta$

How can I then show that any such defined $\delta^+$ is a regular cardinal, where by regular I mean such that $cof(\delta^+)=\delta^+$?

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    What is the problem with the usual proof? – 2017-02-28
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    I don't get how it fits. Since the usual definition of succesor cardinal is $\kappa^+$ for some cardinal $\kappa$ and here we have an ordinal $\delta$ – 2017-02-28
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    I understand the definition is broader than the usual one. I am asking what problems you are finding with the usual proof of regularity of $\kappa^+$. Study the usual proof, see where it does not simply go through unchanged, and check what changes seem needed, at which specific places, for the new version. – 2017-02-28

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