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There are many lambda calculi. THE lambda calculus refers to the original lambda calculus as defined by Church.

Simply typed lambda calculus? Untyped lambda calculus?

How many do you want? If it's eponymous, it has a definite article. The positive integers, are quite distinct from all other sets.

That reminds me of “THE Ohio State University”, contrasting with other Big Ten schools and their common names (Illinois, Indiana, Iowa, Northwestern, Purdue,…) where the THE is often laughed about as hust funny for the reason you cite.

Yes, I went to THE university of York. How dare the other one have the temerity to think it was THE university of York. No no, it's a jumped up teacher training college of Ripon and York St John, made university, just A university of York, not THE.

Also, York University in Canada confused things.

It's quite funny. In the Big Ten unversities (american midwest) it's too late for Ohio State to undo the ongoing humor of "THE Ohio State" because everyone already for decades mocks it as funny and won't let it go.

It’s the lambda calculus as opposed to the pi calculus or some other calculus. <article> <adjective> <noun>

Like the Russian and the Italian?

Like the Russian language and the Italian language.