Square principle
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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:
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 Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): (C_\beta\mid\beta \text{ a limit point of }\kappa^+)
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
- ↑ Lua error in package.lua at line 80: module 'strict' not found., p. 443.
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