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searching for Transfinite induction 16 found (184 total)

Takeuti–Feferman–Buchholz ordinal (423 words) [view diff] exact match in snippet view article find links to article

arithmetic Π 1 1 {\displaystyle \Pi _{1}^{1}} -comprehension + transfinite induction IDω, the system of ω-times iterated inductive definitions Let Ω

Milner–Rado paradox (509 words) [view diff] exact match in snippet view article find links to article

order type at most κn for n a positive integer. The proof is by transfinite induction. Let α {\displaystyle \alpha } be a limit ordinal (the induction

William Alvin Howard (241 words) [view diff] case mismatch in snippet view article find links to article

Genealogy Project. Howard, W. A.; Kreisel, G. (September 1966). "Transfinite Induction and Bar Induction of Types Zero and One, and the Role of Continuity

Algebraic extension (900 words) [view diff] exact match in snippet view article find links to article

extension of K. These finitary results can be generalized using transfinite induction: The union of any chain of algebraic extensions over a base field

Gerhard Gentzen (1,038 words) [view diff] exact match in snippet view article find links to article

done by a direct proof of the unprovability of the principle of transfinite induction, used in his 1936 proof of consistency, within Peano arithmetic

Andrey Muchnik (514 words) [view diff] exact match in snippet view article find links to article

Congress of Mathematicians in Nice. The problem involved eliminating transfinite induction in the proof of Rabin's theorem on the solvability of the monadic

Aronszajn tree (971 words) [view diff] exact match in snippet view article find links to article

Uα for all countable α. We construct the countable levels Uα by transfinite induction on α as follows starting with the empty set as U0: If α + 1 is a

Robert Phelps (1,073 words) [view diff] exact match in snippet view article find links to article

associating with it a partial ordering, and applying to the latter a transfinite induction argument (Zorn's lemma). Phelps has written several advanced monographs

L. E. J. Brouwer (2,157 words) [view diff] exact match in snippet view article find links to article

of intuitionism with respect to "transfinite judgements", e.g. transfinite induction. 1927. L. E. J. Brouwer: "On the domains of definition of functions"

Ovoid (projective geometry) (1,520 words) [view diff] exact match in snippet view article

non-finite projective space the existence of ovoids can be proven using transfinite induction. Any ovoid O {\displaystyle {\mathcal {O}}} in a finite projective

Well-quasi-ordering (3,049 words) [view diff] exact match in snippet view article find links to article

ordinal height o ( v ) {\displaystyle o(v)} , which is defined by transfinite induction as o ( v ) = lim w c h i l d o f v ( o ( w ) + 1 ) {\displaystyle

Mahlo cardinal (2,371 words) [view diff] exact match in snippet view article find links to article

common meaning of 1-inaccessible). Suppose κ is Mahlo. We proceed by transfinite induction on α to show that κ is α-inaccessible for any α ≤ κ. Since κ is

Ordinal arithmetic (4,965 words) [view diff] exact match in snippet view article find links to article

first-order Peano arithmetic: that is, Peano's axioms can show transfinite induction up to any ordinal less than ε0 but not up to ε0 itself). The Cantor

Theories of iterated inductive definitions (2,534 words) [view diff] exact match in snippet view article find links to article

I ( ≺ , F ) {\displaystyle (TI_{\nu }):TI(\prec ,F)} expressing transfinite induction along ≺ {\displaystyle \prec } for an arbitrary L I D ν {\displaystyle

Transseries (5,723 words) [view diff] exact match in snippet view article find links to article

in F ω {\displaystyle F_{\omega }} . Continuing this process by transfinite induction on O r d {\displaystyle \mathbf {Ord} } beyond F ω L E {\displaystyle

Glossary of logic (30,192 words) [view diff] exact match in snippet view article find links to article

formulas, mathematical induction, strong mathematical induction, transfinite induction, weak mathematical induction induction on well-formed formulas A