“Square principle”的意思、由来-开放百科全书

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Square principle

释义

Definition
Variant relative to a cardinal
Notes

In mathematical set theory, the global square principle is a combinatorial principle introduced by Ronald Jensen in his analysis of the fine structure of the constructible universe L.

Definition

Define Sing to be the class of all limit ordinals which are not regular. Global square states that there is a system satisfying:

is a club set of .
ot
If is a limit point of then and

Variant relative to a cardinal

Jensen introduced also a local version of the principle.^[1] If

is an uncountable cardinal,

then asserts that there is a sequence satisfying:

is a club set of .
If , then
If is a limit point of then

Jensen proved that this principle holds in the constructible universe for any uncountable cardinal κ.

Notes

1. ^{{Citation | last1=Jech | first1=Thomas | author1-link=Thomas Jech | title=Set Theory: Third Millennium Edition | publisher=Springer-Verlag | location=Berlin, New York | series=Springer Monographs in Mathematics | isbn=978-3-540-44085-7 | year=2003}}, p. 443.

{{Citation | last1=Jensen | first1=R. Björn | title=The fine structure of the constructible hierarchy | doi=10.1016/0003-4843(72)90001-0 | mr=0309729 | year=1972 | journal=Annals of Mathematical Logic | volume=4 | pages=229–308}}

2 : Set theory|Constructible universe

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