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Uniform versions of some axioms of second order arithmetic
Author(s) -
Sakamoto Nobuyuki,
Yamazaki Takeshi
Publication year - 2004
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.200310122
Subject(s) - mathematics , arithmetic , second order arithmetic , axiom , order (exchange) , peano axioms , discrete mathematics , geometry , finance , economics
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 Σ 0 1 separation are equivalent to (∃ 2 ) over a suitable base theory of higher order arithmetic, where (∃ 2 ) is the assertion that there exists Φ 2 such that Φ f 1 = 0 if and only if ∃ x 0 ( 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. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)