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searching for Kőnig's lemma 8 found (40 total)

Gödel's completeness theorem (2,329 words) [view diff] exact match in snippet view article find links to article

to each other and equivalent to a weak form of choice known as weak Kőnig's lemma, with the equivalence provable in RCA0 (a second-order variant of Peano

Reverse Mathematics: Proofs from the Inside Out (536 words) [view diff] exact match in snippet view article find links to article

namely arithmetical comprehension, recursive comprehension, and the weak Kőnig's lemma. The book is aimed at a "general mathematical audience" including undergraduate

Dialectica interpretation (1,150 words) [view diff] exact match in snippet view article find links to article

monotone and Ferreira-Oliva bounded interpretations (to interpret weak Kőnig's lemma). Comprehensive treatments of the interpretation can be found at, and

Ordinal analysis (4,347 words) [view diff] exact match in snippet view article find links to article

Grzegorczyk hierarchy is total. RCA0, recursive comprehension. WKL0, weak Kőnig's lemma. PRA, primitive recursive arithmetic. IΣ1, arithmetic with induction

Computable analysis (1,553 words) [view diff] case mismatch in snippet view article find links to article

each digit at random in an infinite unending process. Bauer, Andrej. "Kőnig's Lemma and Kleene Tree" (PDF). Yumpu.com. "The Realizability Approach to Computable

Jordan curve theorem (3,270 words) [view diff] exact match in snippet view article find links to article

reverse mathematics the Jordan curve theorem is equivalent to weak Kőnig's lemma over the system R C A 0 {\displaystyle {\mathsf {RCA}}_{0}} . In computational

List of first-order theories (5,269 words) [view diff] exact match in snippet view article find links to article

Recursive Comprehension W K L 0 {\displaystyle {\mathsf {WKL}}_{0}} , Weak Kőnig's lemma A C A 0 {\displaystyle {\mathsf {ACA}}_{0}} , Arithmetical comprehension

Brouwer fixed-point theorem (8,372 words) [view diff] exact match in snippet view article find links to article

the base system RCA0 Brouwer's theorem for a square implies the weak Kőnig's lemma, so this gives a precise description of the strength of Brouwer's theorem