Editing Boolean prime ideal theorem (section)

==References==
*{{citation
 | last1 = Davey | first1 = B. A.
 | last2 = Priestley | first2 = H. A. | author2-link = Hilary Priestley
 | year = 2002
 | title = Introduction to Lattices and Order
 | title-link = Introduction to Lattices and Order
 | edition = 2nd
 | publisher = Cambridge University Press
 | isbn = 978-0-521-78451-1
}}
: ''An easy to read introduction, showing the equivalence of PIT for Boolean algebras and distributive lattices.''

*{{citation
 | last = Johnstone | first = Peter | author-link = Peter Johnstone (mathematician)
 | year = 1982
 | title = Stone Spaces
 | series = Cambridge studies in advanced mathematics
 | publisher = Cambridge University Press
 | isbn = 978-0-521-33779-3
 | volume = 3
}}
: ''The theory in this book often requires choice principles. The notes on various chapters discuss the general relation of the theorems to PIT and MIT for various structures (though mostly lattices) and give pointers to further literature.''

*{{citation
 | last = Banaschewski | first = B.
 | year = 1983
 | title = The power of the ultrafilter theorem
 | journal = [[Journal of the London Mathematical Society]]
 | series = Second Series
 | doi = 10.1112/jlms/s2-27.2.193
 | volume = 27
 | issue = 2
 | pages = 193–202
}}
: ''Discusses the status of the ultrafilter lemma.''

*{{citation
 | last = Erné | first = M.
 | year = 2000
 | title = Prime ideal theory for general algebras
 | journal = Applied Categorical Structures
 | doi = 10.1023/A:1008611926427
 | s2cid = 31605587
 | volume = 8
 | pages = 115–144
 }}
: ''Gives many equivalent statements for the BPI, including prime ideal theorems for other algebraic structures. PITs are considered as special instances of separation lemmas.''

{{Order theory}}

[[Category:Axiom of choice]]
[[Category:Boolean algebra]]
[[Category:Order theory]]
[[Category:Theorems in lattice theory]]