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Mathematically speaking, the contradiction can be avoided by denying that the largest well-ordered type has a successor order type (p. 153; this is analogous to Bernstein 1905b).
"In addition, colleagues in the [legal] profession … report that clients have been sleeping on floors in overcrowded cells – the entirely predictable consequence of law and order type policies".
In this way we have a second order type theory.
Suppose G1 and G2 are of the same order type.
Each transfinite ordinal is the order type of the set of its predecessors; e.g., ω is the order type of {0, 1, 2, 3, …}, and ω+2 is the order type of {0, 1, 2, 3, …, ω, ω+1}.
The second formulation of CH asserts that every well-ordering of the reals has order type less than ℵ2.
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He is a law-and-order type, reared among conservatives….
"I think I'm a top-of-the-order type of guy," Lawton said.
He is a law-and-order type, reared among conservatives in London, and a member of the crew team, whose tastes run to khakis and polo shirts.
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