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While reading "Francis A. Carey, Richard J. Sundberg - Advanced Organic Chemistry Part A. Structure and Mechanisms-Springer (2007)", I came across the following schematic for addition of electrophiles to vinyl ethers:

electrophilic addition to alkoxy alkene

I understand that such a reaction has application in polymer chemistry. For example, under the right acidic conditions, methylvinylether will form polyvinylmethylether:

polymerization of methylvinylether to polyvineylmethylether under acidic conditions

Under what conditions will the electrophile react with the lone-pair of oxygen instead of the $\beta$-Carbon?

In another section, I found that hard-hard and soft-soft interactions are preferred over hard-soft interactions:

hard-hard, soft-soft, and hard-soft interactions

Many questions arise from reading this. Is the lone pair on the oxygen atom hard or soft? And accordingly, what kind of electrophile should be used? Do stearic factors play a role?

It has been pointed out in the comments that addition of electrophile to oxygen is a reversible and non-productive. What I was thinking was something like this:

two electrophilic additions to vinyl ethers

I guess the reaction could be called a vinylic nucleophilic substitution.

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    $\begingroup$ Addition of an electrophile such as a proton to the oxygen of methyl vinyl ether (MVE) is a reversible, non-productive event. MVE in the presence of $\ce{H3O+}$ gives hydrolysis to acetaldehyde. With methanol/$\ce{H+}$ the dimethyl acetal of acetaldehyde is produced. $\endgroup$
    – user55119
    Commented Jul 10, 2022 at 16:35

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