Uniform versions of some axioms of second order arithmetic

Nobuyuki Sakamoto, Takeshi Yamazaki

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

In this paper, we discuss uniform versions of some axioms of second order arithmetic in the context of higher order arithmetic. We prove that uniform versions of weak weak König's lemma WWKL and Σ1 0 separation are equivalent to (∃2) over a suitable base theory of higher order arithmetic, where (∃2) is the assertion that there exists Φ2 such that Φ f1 = 0 if and only if ∃x0 (fx = 0) for all f. We also prove that uniform versions of some well-known theorems are equivalent to (∃2) or the axiom (Suslin) of the existence of the Suslin operator.

Original languageEnglish
Pages (from-to)587-593
Number of pages7
JournalMathematical Logic Quarterly
Volume50
Issue number6
DOIs
Publication statusPublished - 2004 Jan 1
Externally publishedYes

Keywords

  • Higher order arithmetic
  • Reverse mathematics
  • Second order arithmetic
  • Weak König's lemma

ASJC Scopus subject areas

  • Logic

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