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searching for successor ordinal 9 found (31 total)

Iterated forcing (419 words) [view diff] exact match in snippet view article find links to article

α, which give a family of Boolean-valued models VPα. If α+1 is a successor ordinal then Pα+1 is often constructed from Pα using a forcing notion in VPα

Veblen function (2,756 words) [view diff] exact match in snippet view article find links to article

(s_{k})[n]} , φ ( γ ) [ n ] = { n if γ = 1 φ ( γ − 1 ) ⋅ n if γ is a successor ordinal φ ( γ [ n ] ) if γ is a limit ordinal {\displaystyle \varphi (\gamma

Stationary set (930 words) [view diff] exact match in snippet view article find links to article

called an Ulam matrix. H. Friedman has shown that for every countable successor ordinal β{\displaystyle \beta }, every stationary subset of ω1{\displaystyle

Fixed-point lemma for normal functions (650 words) [view diff] exact match in snippet view article find links to article

):\alpha \in A\}} . Indeed, if sup A {\displaystyle \sup A} is a successor ordinal then sup A {\displaystyle \sup A} is an element of A {\displaystyle

Limit cardinal (855 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \aleph _{\alpha ^{+}}=(\aleph _{\alpha })^{+}\,,} if λ is a successor ordinal then ℵ λ {\displaystyle \aleph _{\lambda }} is not a weak limit. Conversely

Kleene's O (2,227 words) [view diff] exact match in snippet view article find links to article

|p|{\displaystyle |p|} is a successor ordinal α+1{\displaystyle \alpha +1}. In Kleene's O{\displaystyle {\mathcal {O}}}, a successor ordinal is defined in terms

Absoluteness (logic) (1,259 words) [view diff] exact match in snippet view article

is the empty set. x is an ordinal. x is a finite ordinal. x is a successor ordinal. x is a limit ordinal. x = ω. x is (the graph of) a function. Other

Zorn's lemma (3,678 words) [view diff] exact match in snippet view article find links to article

case) or by appending b(S) to the "last" S (corresponding to the successor ordinal case). This proof shows that actually a slightly stronger version

Buchholz psi functions (4,794 words) [view diff] exact match in snippet view article find links to article

} -th element of this sequence. If α {\displaystyle \alpha } is a successor ordinal then cof ⁡ ( α ) = 1 {\displaystyle \operatorname {cof} (\alpha )=1}