# What year was Hechler forcing created?

Hechler forcing is described on page 278, Jech.

Does anyone know when Hechler forcing was first used in a publication?

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Incidentally, Erin, Hechler sometimes shows up at our seminar, although it has been a while since I've seen him. –  Joel David Hamkins Apr 16 '14 at 20:19
That's awesome, I hope I get to talk to him someday. –  Erin Carmody Apr 17 '14 at 0:31

The citation is given on page 283 of Jech (at least, in the 3rd Millenium edition); it is to Hechler's paper "On the existence of certain cofinal subsets of $^\omega\omega$," in the collection "Axiomatic Set Theory II" (see http://www.ams.org/books/pspum/013.2/9987/pspum9987.pdf), which is the only paper by Hechler in Jech's bibliography. It is somewhat difficult to read, but I think that we call "Hechler forcing" is a simplified version of the forcing introduced on page 159 of that paper; it seems reasonable to assume that this is its first instance.
In connection with "somewhat difficult to read", it may be worth reminding people that the 1967 symposium was, I believe, where both Shoenfield's unramified forcing and Scott and Solovay's Boolean-valued models were first presented. Before then, forcing was usually done in the style of Cohen's original work, using a ramified language of terms in a forcing extension of $L$, using strong rather than weak forcing (strong forcing doesn't respect classical logic), etc. No wonder it was difficult to read. (Young people nowadays don't realize how good they have it.) –  Andreas Blass Apr 28 '14 at 0:31