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shrewd
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The answer SHREWD has 125 possible clue(s) in existing crosswords.
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Definitions of shrewd in various dictionaries:
adj - marked by practical hardheaded intelligence
adj - used of persons
Characterized by keen awareness, sharp intelligence, and often a sense of the practical.
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Keep reading for additional results and analysis below.
| Possible Crossword Clues |
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| Canny |
| Calculating |
| Astute |
| Insightful |
| Sharp |
| Slick |
| Clever |
| Cagey |
| Street-smart |
| Exceedingly clever |
| Possible Jeopardy Clues |
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| This adjective that means "cunning" probably comes from the name of a "tamed" insectivore |
| Shrewd description |
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In mathematics, a shrewd cardinal is a certain kind of large cardinal number introduced by (Rathjen 1995)., extending the definition of indescribable cardinals. * A cardinal number κ is called λ-shrewd if for every proposition φ, and set A ⊆ Vκ with (Vκ+λ, ∈, A) ⊧ φ there exists an α, λ' < κ with (Vα+λ', ∈, A ∩ Vα) ⊧ φ. It is called shrewd if it is λ-shrewd for every λ (including λ > κ). * This definition extends the concept of indescribability to transfinite levels. A λ-shrewd cardinal is also μ-shrewd for any ordinal μ < λ. Shrewdness was developed by Michael Rathjen as part of his ordinal analysis of Π12-comprehension. It is essentially the nonrecursive analog to the stability property for admissible ordinals. * More generally, a cardinal number κ is called λ-Πm-shrewd if for every Πm proposition φ, and set A ⊆ Vκ with (Vκ+λ, ∈, A) ⊧ φ there exists an α, λ' < κ with (Vα+λ', ∈, A ∩ Vα) ⊧ φ. * Here one looks at formulas with m-1 alternations of quantifiers with the outermost quantifier being universal. * For finite n, an n-Πm-shrewd cardinals is the same thing as a Πmn-indescribable cardinal. * If κ is a subtle cardinal, then the set of κ-shrewd cardinals is stationary in κ. Rathjen does not state how shrewd cardinals compare to unfoldable cardinals, however. * λ-shrewdness is an improved version of λ-indescribability, as defined in Drake; this cardinal property differs in that the reflected substructure must be (Vα+λ, ∈, A ∩ Vα), making it impossible for a cardinal κ to be κ-indescribable. Also, the monotonicity property is lost: a λ-indescribable cardinal may fail to be α-indescribable for some ordinal α < λ. |